Structural progressive collapse fragility assessment method combining static and dynamic probabilistic analysis

Abstract

Disclosed in the present invention is a structural progressive collapse fragility assessment method combining static and dynamic probabilistic analysis. The method comprises the following steps: (1) acquiring design parameters affecting structural progressive collapse resistance, to obtain a design parameter sample set; (2) constructing corresponding deterministic numerical models for static and dynamic progressive collapse, and on the basis of the sample set, establishing a corresponding sub-model; (3) performing Pushdown analysis; (4) performing non-linear displacement time-history analysis under the action of different load intensities; (5) performing fitting to obtain a probability density function of the structural progressive collapse resistance, and calculating a corresponding mean value and standard deviation; (6) performing fitting to obtain a probability density function of a structural progressive collapse load effect, and calculating a corresponding mean value and standard deviation; (7) obtaining structural progressive collapse fragility scatter points; and (8) fitting, by means of regression analysis, obtained scatter points of exceedance probability corresponding to load coefficients, in order to obtain a structural progressive collapse fragility curve. The present invention can achieve more accurate fragility assessment results.

Description

A method for assessing the progressive collapse vulnerability of structures by combining static and dynamic probabilistic analysis Technical Field

[0001] This invention relates to the field of structural uncertainty quantification technology, specifically to a method and system for assessing the vulnerability of structures to progressive collapse by combining static and dynamic probability analysis. Background Technology

[0002] Alternate load path analysis is a primary method for assessing the progressive collapse resistance of structures. This method first removes critical structural components to simulate local failures in the system, then predicts the structural response through nonlinear static or dynamic analysis to determine whether the structure will fail. However, understanding the catastrophic behavior of a structure solely through deterministic conditions cannot account for uncertainties in the structural system and external loads. Furthermore, existing methods for assessing progressive collapse vulnerability from an uncertainty perspective are mostly based on static column removal conditions. Incremental dynamic analysis (IDA) based on dynamic instantaneous analysis is also used to analyze the vulnerability of structures under dynamic column removal conditions. This method has been widely used in the uncertainty analysis of dynamic progressive collapse, but existing progressive collapse vulnerability analysis techniques often use the structural performance analysis results under deterministic analysis as a threshold. Current methods for assessing progressive collapse vulnerability still have some shortcomings. On the one hand, according to the theory of stochastic reliability of structures, the probability of structural failure depends on the uncertainties of both resistance and load effects. However, current vulnerability analysis methods are mostly based on static or dynamic analysis, which can only reflect one of the stochastic influences of resistance or load effects. On the other hand, the thresholds for different limit states in existing progressive collapse dynamic vulnerability analysis are mostly fixed values ​​given in the code. However, the dispersion of the progressive collapse resistance of a structure at different development stages will seriously affect the threshold. Directly using the threshold in the code may greatly underestimate the possibility of structural failure. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a method for assessing the progressive collapse vulnerability of structures by combining static and dynamic probabilistic analysis. It combines the probabilistic analysis of progressive collapse resistance and load effects, and evaluates the exceedance probability of structures under different limit states through the convolution integral method, so as to solve the problems existing in the background technology.

[0004] Technical solution: The present invention provides a method for assessing the progressive collapse vulnerability of structures by combining static and dynamic probabilistic analysis, comprising the following steps:

[0005] (1) Obtain the design parameters affecting the progressive collapse resistance of the structure as random variables, denoted as X=(X1,X2,…,X…). n ) TWhere n is the number of random variables; design parameter sample set;

[0006] (2) Construct corresponding static and dynamic progressive collapse deterministic numerical models; establish corresponding sub-models based on the sample set;

[0007] (3) Based on the model constructed in step (2), perform Pushdown analysis;

[0008] (4) Based on the model constructed in step (2), perform nonlinear displacement time history analysis under different load intensities;

[0009] (5) Based on the normal distribution assumption, the probability density function of the resistance to continuous collapse of the structure is fitted; and the corresponding mean and standard deviation are calculated to determine the threshold of the structure under different performance levels after considering static uncertainty.

[0010] (6) Based on the log-normal distribution assumption, the probability density function of the continuous collapse load effect of the structure is fitted; and the corresponding mean and standard deviation are calculated to determine the probabilistic load effect of the structure under different performance levels after considering dynamic uncertainty.

[0011] (7) Obtain the scatter plot of the structural continuous collapse vulnerability;

[0012] (8) Based on the log-normal distribution assumption, the continuous collapse vulnerability curve of the structure is obtained by fitting the exceedance probability scatter points corresponding to each load coefficient obtained in step (7) through regression analysis.

[0013] Furthermore, in step (1), Latin hypercube sampling is used to generate a sample set of sub-model design parameters with a sample size of 1000; where the mean of each random variable is the initial design value.

[0014] Further, step (3) is as follows: The entire pushdown analysis process is controlled by the incremental gravity load applied to the structure until the structure collapses; the vertical displacement Δ is applied proportionally to the beam-column joint, and the gravity load change of the damaged span is recorded to obtain the corresponding pushdown curve; the displacement corresponding to different limit states is determined through the pushdown curve, denoted as Δ. R .

[0015] Further, step (4) is as follows: the gravity load applied to the structure is used as a strength index, and the vertical displacement of the beam-column joint at the top of the removed column is used as a damage index; by changing the load factor α, the gravity load applied to the damaged span is gradually increased, and the vertical displacement of the beam-column joint at the top of the removed column corresponding to different limit states is recorded and denoted as Δ. S .

[0016] Furthermore, the formula for the progressive collapse vulnerability of the structure in step (7) is as follows: P[S≥R|IM=im]=Pr[R≤S|IM=im] (1)

[0017] Where S is the structural load effect, and R is the continuous collapse resistance corresponding to a certain ultimate state of the structure; Formula (1) is rewritten as: P[S≥R|IM=im]=∫ R≤S dF RS (r,s)=∫∫ R≤S f RS (r,s)drds (2)

[0018] Among them, F RS (r,s) and f RS (r,s) are the joint cumulative density function and joint probability density function of R and S, respectively;

[0019] For simplified calculations, assuming R and S are independent, the final structural progressive collapse vulnerability can be calculated using the following formula:

[0020] The probability density function μ of the structural continuous collapse resistance obtained in steps (5) and (6) is used to... R σ, the probability density function of resistance to progressive collapse of a structure R The probability density function μ of the load effect of the structure in progressive collapse S and the probability density function σ of the load effect of the structure in continuous collapse S Substituting into formula (3), the probability of the structure exceeding a certain limit state under a certain load coefficient can be obtained by using the convolution integral method, that is, the scatter plot of the structural continuous collapse vulnerability.

[0021] The present invention discloses a structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis, comprising:

[0022] Acquisition Module: Used to acquire design parameters affecting the progressive collapse resistance of a structure as random variables, denoted as X = (X1, X2, ..., X...). n ) T Where n is the number of random variables; design parameter sample set;

[0023] The deterministic numerical model module for progressive collapse is used to construct corresponding static and dynamic deterministic numerical models for progressive collapse and to establish corresponding sub-models based on the sample set.

[0024] Pushdown module: Used for pushdown analysis based on the model built in the progressive collapse deterministic numerical model module;

[0025] Nonlinear displacement time history analysis module: used to perform nonlinear displacement time history analysis under different load intensities based on the model built in the progressive collapse deterministic numerical model module;

[0026] The module for the probability density function of resistance to progressive collapse of a structure is used to fit the probability density function of resistance to progressive collapse of a structure based on the assumption of normal distribution; and to calculate the corresponding mean and standard deviation, and to determine the threshold of the structure at different performance levels after considering static uncertainties.

[0027] The module for probability density function of load effect of progressive collapse structure is used to fit the probability density function of load effect of progressive collapse structure based on the log-normal distribution assumption; and to calculate the corresponding mean and standard deviation to determine the probabilistic load effect of structure under different performance levels after considering dynamic uncertainties.

[0028] Progressive Collapse Vulnerability Scatter Module: Used to obtain scatter points of progressive collapse vulnerability of structures;

[0029] The progressive collapse vulnerability curve module is used to obtain the progressive collapse vulnerability curve of a structure based on the log-normal distribution assumption and by fitting the exceedance probability scatter points corresponding to each load coefficient through regression analysis.

[0030] Furthermore, in the acquisition module, Latin hypercube sampling is used to generate a sample set of sub-model design parameters with a sample size of 1000; the mean of each random variable is the initial design value.

[0031] Furthermore, in the Pushdown module, the specific steps are as follows: The entire Pushdown analysis process is controlled by the incremental gravity load applied to the structure until the structure collapses; the vertical displacement Δ is applied proportionally to the beam-column joints, and the change in gravity load in the damaged span is recorded to obtain the corresponding Pushdown curve; the displacement corresponding to different ultimate states is determined through the Pushdown curve, denoted as Δ. R .

[0032] Furthermore, in the nonlinear displacement time history analysis module, the specific steps are as follows: the gravity load applied to the structure is used as a strength index, and the vertical displacement of the beam-column joint at the top of the removed column is used as a damage index; by changing the load factor α, the gravity load applied to the damaged span is gradually increased, and the vertical displacement of the beam-column joint at the top of the removed column corresponding to different limit states is recorded, denoted as Δ. S .

[0033] Furthermore, in the progressive collapse vulnerability scatter plot module, the formula for the progressive collapse vulnerability of a structure is as follows: P[S≥R|IM=im]=Pr[R≤S|IM=im] (1)

[0034] Where S is the structural load effect, and R is the continuous collapse resistance corresponding to a certain ultimate state of the structure; Formula (1) is rewritten as: P[S≥R|IM=im]=∫ R≤S dF RS (r,s)=∫∫ R≤S f RS (r,s)drds (2)

[0035] Among them, F RS (r,s) and f RS (r,s) are the joint cumulative density function and joint probability density function of R and S, respectively;

[0036] For simplified calculations, assuming R and S are independent, the final structural progressive collapse vulnerability can be calculated using the following formula:

[0037] The obtained probability density function of the structural continuous collapse resistance μ R σ, the probability density function of resistance to progressive collapse of a structure R The probability density function μ of the load effect of the structure in progressive collapse S and the probability density function σ of the load effect of the structure in continuous collapse S Substituting into formula (3), the probability of the structure exceeding a certain limit state under a certain load coefficient can be obtained by using the convolution integral method, that is, the scatter plot of the structural continuous collapse vulnerability.

[0038] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: It characterizes the inherent variability of the structure and the randomness of external loads through Latin hypercube sampling; it utilizes pushdown analysis and IDA to consider the uncertainties in the progressive collapse resistance and load effects of the structure at different performance levels, further providing guidance for the probabilistic assessment of the structure's progressive collapse resistance. This invention overcomes the limitation of traditional progressive collapse vulnerability analysis methods that cannot simultaneously consider the uncertainties in structural performance and demand. By integrating the probabilistic behavior of structural resistance and load effects into the vulnerability analysis framework through convolutional integral methods, it can obtain more accurate progressive collapse vulnerability assessment results. Attached Figure Description

[0039] Figure 1 is a flowchart of the present invention;

[0040] Figure 2 is a schematic diagram of the structural prototype of the present invention;

[0041] Figure 3 is a Pushdown curve diagram of the present invention; wherein, Figure 3(a) is the case of removing column A; Figure 3(b) is the case of removing column B;

[0042] Figure 4 is a histogram of ΔR and a probability density function PDF curve of the present invention; wherein, (a) in Figure 4 shows the normal operation of the demolition of column A; (b) in Figure 4 shows the collapse prevention of the demolition of column A; (c) in Figure 4 shows the normal operation of the demolition of column B; and (d) in Figure 4 shows the collapse prevention of the demolition of column B.

[0043] Figure 5 shows the Δ corresponding to different load factors of the present invention. S Histograms and PDF curves; in Figure 5(a), the demolition of column A is shown; in Figure 5(b), the demolition of column B is shown.

[0044] Figure 6 shows the fragility curves obtained by the present invention and the prior art; where (a) in Figure 6 is based on the Pushdown method; and (b) in Figure 6 is based on the IDA method. Detailed Implementation

[0045] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0046] As shown in Figure 1, this embodiment of the invention provides a method for assessing the progressive collapse vulnerability of structures by combining static and dynamic probabilistic analysis, comprising the following steps:

[0047] Step 1: Select the design parameters that affect the progressive collapse resistance of the structure as random variables, denoted as X = (X1, X2, ..., X...). n ) T Where n is the number of random variables. Subsequently, Latin hypercube sampling is used to generate a sample set of sub-model design parameters with a sample size of 1000. The mean of each random variable is the initial design value; the corresponding coefficient of variation and the distribution assumptions they follow will be given later.

[0048] Step 2: Select a specific demolition column case and establish corresponding deterministic numerical models for static and dynamic progressive collapse. Establish corresponding sub-models based on the sample set.

[0049] Step 3: Based on all static progressive collapse sub-models, conduct pushdown analysis. The entire pushdown analysis process is controlled by incremental gravity loads applied to the structure until collapse. However, only the gravity load on the beams adjacent to the demolished columns increases; the loads on the remaining beams remain unchanged from the initial design loads. Vertical displacement Δ is applied proportionally to the beam-column joints, and the change in gravity load in the damaged span is recorded to obtain the corresponding pushdown curve. The displacement corresponding to different ultimate states is determined through the pushdown curve, denoted as Δ. R .

[0050] Step 4: Based on all dynamic progressive collapse sub-models, conduct nonlinear displacement time history analysis under different load intensities. The gravity load applied to the structure is used as the strength index, and the vertical displacement of the beam-column joint at the top of the demolished column is used as the damage index. By changing the load factor α, the gravity load applied to the damaged span is gradually increased, and the vertical displacement of the beam-column joint at the top of the demolished column corresponding to different ultimate states is recorded, denoted as Δ. S .

[0051] Step 5, based on the normal distribution assumption, according to the recorded Δ R The probability density function of the resistance to progressive collapse of the structure was obtained by fitting the data, and the corresponding mean μ was calculated. R and standard deviation σ R The threshold values ​​of the structure at different performance levels after considering static uncertainties were determined.

[0052] Step 6, based on the log-normal distribution assumption, according to the recorded Δ S The probability density function of the load effect of the structure in continuous collapse was obtained by fitting, and the corresponding mean μ was calculated. S and standard deviation σ S The probabilistic load effects of the structure at different performance levels were determined after considering dynamic uncertainties.

[0053] Step 7, the structural progressive collapse vulnerability can be expressed as: P[S≥R|IM=im]=Pr[R≤S|IM=im] (1)

[0054] Where S represents the structural load effect, and R represents the progressive collapse resistance corresponding to a certain ultimate state of the structure. Furthermore, equation (1) can be written as: P[S≥R|IM=im]=∫ R≤S dF RS (r,s)=∫∫ R≤S f RS (r,s)drds (2)

[0055] Among them, F RS (r,s) and f RS (r,s) are the joint cumulative density function and joint probability density function of R and S, respectively.

[0056] To simplify the calculation, we assume that R and S are independent. The final progressive collapse vulnerability of the structure can be calculated using the following formula:

[0057] The μ obtained in steps (5) and (6) R σ R μ S and σ SSubstituting into equation (3), the probability of the structure exceeding a certain limit state under a certain load coefficient can be obtained by using the convolution integral method, that is, the scatter plot of the structural continuous collapse vulnerability.

[0058] Step 8: Based on the log-normal distribution assumption, the continuous collapse vulnerability curve of the structure is obtained by fitting the exceedance probability scatter points corresponding to each load coefficient obtained in step (7) through regression analysis.

[0059] Taking a two-dimensional 10-story, 5-span RC frame structure as an example, considering the failure of the bottom corner columns and edge columns, denoted as column A and column B respectively, the structural prototype and reinforcement details are shown in Figure 2. First, the main parameters affecting the progressive collapse resistance of the structure are selected, including 13 random parameters related to geometric dimensions, material properties, and load effects. Assuming that the random variables are independent, Latin hypercube sampling is conducted, and corresponding numerical simulations are performed. During the sampling process, the mean of each variable is taken as the structural design value. The coefficients of variation and the distribution functions of each random variable are based on relevant classical studies, detailed in Table 1. The shape coefficients α and β of the β distribution are 3.2 and 4.28, respectively. Meanwhile, due to the large number of types of structural beam / column reinforcement design values, specific mean values ​​are not given.

[0060] Table 1. Random parameter distribution of a 10-story RC frame structure

[0061] Figure 3 shows the stochastic pushdown curve of the structure, where Figure 3(a) and Figure 3(b) represent the demolition of column A and column B, respectively. Figure 4 shows the Δ R Histograms and probability density function (PDF) curves are shown in Figures 3 and 4, where Figures 4(a) and 4(b) represent the NO and CP limit states for the removal of column A, respectively; Figures 4(c) and 4(d) represent the NO and CP limit states for the removal of column B, respectively. From Figures 3 and 4, it can be seen that during the arch compression stage, σ... R The change is relatively small, but when the structure enters the catenary stage, σ C The magnitude of change increases rapidly. Under the two scenarios of column A and column B removal, the σ value of the NO limiting state... R Both are less than σ in the CP limiting state. R After removing column A, the σ corresponding to the limiting states of NO and CP... R The values ​​are 0.009 and 0.081 respectively, with the latter being nine times the former. In the case of B-pillar removal, NO(σ) R =0.007) and CP(σ R =0.082) σ in the limit state R The difference is significant; σ in the CP limiting state RThis is 11.7 times that of the NO limit state. These results demonstrate the significant impact of uncertainty on the progressive collapse capability of a structure, especially during the catenary action phase. Therefore, stochastic analysis under static demolition column conditions is needed to determine the threshold values ​​for different limit states of the structure.

[0062] Figure 5 shows the Δ corresponding to different load factors. S The histograms and PDF curves are shown in Figures 5(a) and 5(b), respectively, for the cases of removing column A and column B. As can be seen from Figure 5, with the increase of the load factor, the PDF curve tilts more significantly to the left, and the dispersion is also greater. This is because most sub-models can maintain equilibrium and avoid failure under smaller load factors. When the structure is subjected to a larger gravity load, although the peak PDF still appears within a smaller displacement range, the increased proportion of collapsed structures leads to an increased frequency of large deformations, thus exhibiting an asymmetric trend.

[0063] Figure 6 shows the vulnerability curves obtained by our proposed method and existing methods (based on the Pushdown method and the IDA method), where Figure 6(a) and Figure 6(b) represent the cases of removing column A and column B, respectively. Table 2 summarizes the load factors corresponding to a failure probability of 50%. The results show that the NO limit state vulnerability curve calculated by our proposed method lies between the vulnerability curves obtained by the IDA and Pushdown methods, while the CP limit state curve shifts to the left. In the scenarios of removing column A and column B, the S-values ​​of the NO limit state calculated by our proposed method are 0.921 and 0.887, respectively. The difference in S-values ​​between the vulnerability curves calculated by our proposed method and those obtained by the Pushdown method is much greater than the difference between the curves obtained by the IDA method, reaching 30.29% and 33.26%, respectively. For the CP limit state, in the scenarios of removing column A and column B, the S-values ​​obtained by the proposed framework are 1.343 and 1.359, respectively. Compared to the corresponding vulnerability curves based on Pushdown and IDA, the average changes in S are -10.92% and -8.64%, respectively, indicating that under the same load intensity, the failure probability of the structure is higher when considering both performance and demand uncertainties. Compared to our method, the results obtained from vulnerability analysis of progressively collapsing structures under static and dynamic column removal scenarios using existing methods are more conservative. The significant differences in the vulnerability curves also demonstrate the necessity of considering both capacity and demand uncertainties in the progressive collapse analysis of structures.

[0064] Table 2 shows the S values ​​of the fragility curves obtained using this method and existing methods.

[0065] This invention also provides a structural progressive collapse vulnerability assessment system that combines static and dynamic probabilistic analysis, comprising:

[0066] Acquisition Module: Used to acquire design parameters affecting the progressive collapse resistance of a structure as random variables, denoted as X = (X1, X2, ..., X...). n ) T , where n is the number of random variables; design parameter sample set; where Latin hypercube sampling is used to generate the corresponding sampling of the sub-model design parameter sample set, with a sample size of 1000; where the mean of each random variable is the initial design value.

[0067] The deterministic numerical model module for progressive collapse is used to construct corresponding static and dynamic deterministic numerical models for progressive collapse and to establish corresponding sub-models based on the sample set.

[0068] The Pushdown module is used to perform pushdown analysis on models built in the progressive collapse deterministic numerical model module. Specifically, the entire pushdown analysis process is controlled by incremental gravity loads applied to the structure until collapse. Vertical displacement Δ is applied proportionally to the beam-column nodes, and the gravity load changes in the damaged span are recorded to obtain the corresponding pushdown curves. The displacements corresponding to different ultimate states are determined using the pushdown curves, denoted as Δ. R .

[0069] Nonlinear Displacement Time History Analysis Module: Used to perform nonlinear displacement time history analysis under different load intensities based on the model constructed in the progressive collapse deterministic numerical model module; In detail: the gravity load applied to the structure is used as the strength index, and the vertical displacement of the beam-column joint at the top of the demolished column is used as the damage index; by changing the load factor α, the gravity load applied to the damaged span is gradually increased, and the vertical displacement of the beam-column joint at the top of the demolished column corresponding to different ultimate states is recorded, denoted as Δ. S .

[0070] The module for the probability density function of resistance to progressive collapse of a structure is used to fit the probability density function of resistance to progressive collapse of a structure based on the assumption of normal distribution; and to calculate the corresponding mean and standard deviation, and to determine the threshold of the structure at different performance levels after considering static uncertainties.

[0071] The module for probability density function of load effect of progressive collapse structure is used to fit the probability density function of load effect of progressive collapse structure based on the log-normal distribution assumption; and to calculate the corresponding mean and standard deviation to determine the probabilistic load effect of structure under different performance levels after considering dynamic uncertainties.

[0072] Progressive collapse vulnerability scatter plot module: used to obtain progressive collapse vulnerability scatter plots of structures; the progressive collapse vulnerability formula of structures is as follows: P[S≥R|IM=im]=Pr[R≤S|IM=im] (1)

[0073] Where S is the structural load effect, and R is the continuous collapse resistance corresponding to a certain ultimate state of the structure; Formula (1) is rewritten as: P[S≥R|IM=im]=∫ R≤S dF RS (r,s)=∫∫ R≤S f RS (r,s)drds (2)

[0074] Among them, F RS (r,s) and f RS (r,s) are the joint cumulative density function and joint probability density function of R and S, respectively;

[0075] For simplified calculations, assuming R and S are independent, the final structural progressive collapse vulnerability can be calculated using the following formula:

[0076] The obtained probability density function of the structural continuous collapse resistance μ R σ, the probability density function of resistance to progressive collapse of a structure R The probability density function μ of the load effect of the structure in progressive collapse S and the probability density function σ of the load effect of the structure in continuous collapse S Substituting into formula (3), the probability of the structure exceeding a certain limit state under a certain load coefficient can be obtained by using the convolution integral method, that is, the scatter plot of the structural continuous collapse vulnerability.

[0077] The progressive collapse vulnerability curve module is used to obtain the progressive collapse vulnerability curve of a structure based on the log-normal distribution assumption and by fitting the exceedance probability scatter points corresponding to each load coefficient through regression analysis.

Claims

1. A method for assessing the progressive collapse vulnerability of structures by combining static and dynamic probabilistic analysis, characterized in that, Includes the following steps: (1) Obtain the design parameters affecting the progressive collapse resistance of the structure as random variables, denoted as X=(X1,X2,…,X…). n ) T Where n is the number of random variables; design parameter sample set; (2) Construct corresponding static and dynamic progressive collapse deterministic numerical models; establish corresponding sub-models based on the sample set; (3) Based on the model constructed in step (2), perform Pushdown analysis; (4) Based on the model constructed in step (2), perform nonlinear displacement time history analysis under different load intensities; (5) Based on the normal distribution assumption, the probability density function of the resistance to continuous collapse of the structure is fitted; and the corresponding mean and standard deviation are calculated to determine the threshold of the structure under different performance levels after considering static uncertainty. (6) Based on the log-normal distribution assumption, the probability density function of the continuous collapse load effect of the structure is fitted; and the corresponding mean and standard deviation are calculated to determine the probabilistic load effect of the structure under different performance levels after considering dynamic uncertainty. (7) Obtain the scatter plot of the structural continuous collapse vulnerability; (8) Based on the log-normal distribution assumption, the continuous collapse vulnerability curve of the structure is obtained by fitting the exceedance probability scatter points corresponding to each load coefficient obtained in step (7) through regression analysis.

2. The structural progressive collapse vulnerability assessment method combining static and dynamic probabilistic analysis according to claim 1, characterized in that, In step (1), Latin hypercube sampling is used to generate a sample set of sub-model design parameters with a sample size of 1000; the mean of each random variable is the initial design value.

3. The structural progressive collapse vulnerability assessment method combining static and dynamic probabilistic analysis according to claim 1, characterized in that, Step (3) is as follows: The entire Pushdown analysis process is controlled by the incremental gravity load applied to the structure until the structure collapses; the vertical displacement Δ is applied proportionally to the beam-column joint, and the change in gravity load in the damaged span is recorded to obtain the corresponding Pushdown curve; the displacement corresponding to different limit states is determined through the Pushdown curve, denoted as Δ. R .

4. The structural progressive collapse vulnerability assessment method combining static and dynamic probabilistic analysis according to claim 1, characterized in that, Step (4) is as follows: The gravity load applied to the structure is used as the strength index, and the vertical displacement of the beam-column joint at the top of the demolished column is used as the damage index; by changing the load factor α, the gravity load applied to the damaged span is gradually increased, and the vertical displacement of the beam-column joint at the top of the demolished column corresponding to different limit states is recorded and denoted as Δ. S .

5. The structural progressive collapse vulnerability assessment method combining static and dynamic probabilistic analysis according to claim 1, characterized in that, The formula for the progressive collapse vulnerability of the structure in step (7) is as follows: P[S≥R|IM=im]=Pr[R≤S|IM=im] (1) Where S is the structural load effect, and R is the continuous collapse resistance corresponding to a certain ultimate state of the structure; Formula (1) is rewritten as: P[S≥R|IM=im]=∫ R≤S dF RS (r,s)=∫∫ R≤S f RS (r,s)drds (2) Among them, F RS (r,s) and f RS (r,s) are the joint cumulative density function and joint probability density function of R and S, respectively; For simplified calculations, assuming R and S are independent, the final structural progressive collapse vulnerability can be calculated using the following formula: The probability density function μ of the structural continuous collapse resistance obtained in steps (5) and (6) is used to... R σ, the probability density function of resistance to progressive collapse of a structure R The probability density function μ of the load effect of the structure in progressive collapse S and the probability density function σ of the load effect of the structure in continuous collapse S Substituting into formula (3), the probability of the structure exceeding a certain limit state under a certain load coefficient can be obtained by using the convolution integral method, that is, the scatter plot of the structural continuous collapse vulnerability.

6. A structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis, used to perform the structural progressive collapse vulnerability assessment method as described in any one of claims 1-5, characterized in that, The structural progressive collapse vulnerability assessment system includes: Acquisition Module: Used to acquire design parameters affecting the progressive collapse resistance of a structure as random variables, denoted as X = (X1, X2, ..., X...). n ) T Where n is the number of random variables; design parameter sample set; The deterministic numerical model module for progressive collapse is used to construct corresponding static and dynamic deterministic numerical models for progressive collapse and to establish corresponding sub-models based on the sample set. Pushdown module: Used for pushdown analysis based on the model built in the progressive collapse deterministic numerical model module; Nonlinear displacement time history analysis module: used to perform nonlinear displacement time history analysis under different load intensities based on the model built in the progressive collapse deterministic numerical model module; The module for the probability density function of resistance to progressive collapse of a structure is used to fit the probability density function of resistance to progressive collapse of a structure based on the assumption of normal distribution; and to calculate the corresponding mean and standard deviation, and to determine the threshold of the structure at different performance levels after considering static uncertainties. The module for probability density function of load effect of progressive collapse structure is used to fit the probability density function of load effect of progressive collapse structure based on the log-normal distribution assumption; and to calculate the corresponding mean and standard deviation to determine the probabilistic load effect of structure under different performance levels after considering dynamic uncertainties. Progressive Collapse Vulnerability Scatter Module: Used to obtain scatter points of progressive collapse vulnerability of structures; The progressive collapse vulnerability curve module is used to obtain the progressive collapse vulnerability curve of a structure based on the log-normal distribution assumption and by fitting the exceedance probability scatter points corresponding to each load coefficient through regression analysis.

7. The structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 6, characterized in that... In the acquisition module, Latin hypercube sampling is used to generate a sample set of sub-model design parameters with a sample size of 1000; the mean of each random variable is the initial design value.

8. The structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 6, characterized in that... In the Pushdown module, the specific steps are as follows: The entire Pushdown analysis process is controlled by the incremental gravity load applied to the structure until the structure collapses; the vertical displacement Δ is applied proportionally to the beam-column joints, and the change in gravity load in the damaged span is recorded to obtain the corresponding Pushdown curve; the displacement corresponding to different ultimate states is determined through the Pushdown curve, denoted as Δ. R .

9. The structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 6, characterized in that, In the nonlinear displacement time history analysis module, the specific steps are as follows: The gravity load applied to the structure is used as a strength index, and the vertical displacement of the beam-column joint at the top of the removed column is used as a damage index; by changing the load factor α, the gravity load applied to the damaged span is gradually increased, and the vertical displacement of the beam-column joint at the top of the removed column corresponding to different limit states is recorded and denoted as Δ. S .

10. A structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 6, characterized in that, In the progressive collapse vulnerability scatter plot module, the formula for the progressive collapse vulnerability of a structure is as follows: P[S≥R|IM=im]=Pr[R≤S|IM=im] (1) Where S is the structural load effect, and R is the continuous collapse resistance corresponding to a certain ultimate state of the structure; Formula (1) is rewritten as: P[S≥R|IM=im]=∫ R≤S dF RS (r,s)=∫∫ R≤S f RS (r,s)drds (2) Among them, F RS (r,s) and f RS (r,s) are the joint cumulative density function and joint probability density function of R and S, respectively; For simplified calculations, assuming R and S are independent, the final structural progressive collapse vulnerability can be calculated using the following formula: The obtained probability density function of the structural continuous collapse resistance μ R σ, the probability density function of resistance to progressive collapse of a structure R The probability density function μ of the load effect of the structure in progressive collapse S and the probability density function σ of the load effect of the structure in continuous collapse S Substituting into formula (3), the probability of the structure exceeding a certain limit state under a certain load coefficient can be obtained by using the convolution integral method, that is, the scatter plot of the structural continuous collapse vulnerability.

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