Time-varying Vulnerability Analysis Method of Cable-stayed Bridges Based on Structural Configuration and Bayesian Network

Abstract

The present invention relates to a time-varying vulnerability analysis method for cable-stayed bridges based on structural configuration and Bayesian networks, comprising the following steps: Step S1: Define external loads, cable-stayed bridge systems, and each component as nodes of a variable-structure discrete dynamic Bayesian network (VDDBN), and pre-define the VDDBN topology; Step S2: Consider the time-varying models and their uncertainties of structural parameters and external loads, and construct the VDDBN through parameter learning; Step S3: Input evidence into the VDDBN to infer the posterior probabilities of all nodes in all time slices, calculate the vulnerability probabilities of components to establish time-varying vulnerability curves of components, and finally establish the time-varying vulnerability curve of the structure through clustering. The present invention can effectively analyze the changes in the vulnerability of cable-stayed bridge systems over time history, providing reliable data for the safety and reliability of cable-stayed bridge systems.

Description

Technical Field

[0001] The present invention relates to the field of structural vulnerability analysis, and particularly to a time-varying vulnerability analysis method for cable-stayed bridges based on structural configuration and Bayesian network. Background Art

[0002] Civil engineering structures should be able to withstand various actions that may occur during their normal service life, and when accidental events occur, the structures should not suffer disproportionate damage compared to the cause. Vulnerability is an embodiment of this performance of the structure, that is, structures with high vulnerability are more likely to collapse under emergency events (such as explosions, earthquakes, typhoons, etc.). Currently, the domestic and foreign research on vulnerability mainly focuses on two aspects: structural vulnerability and seismic vulnerability. The main difference between the two is that seismic vulnerability pays more attention to the probability of the structure exceeding a certain damage state under seismic loads, which is usually quantitatively represented by a seismic vulnerability curve, while structural vulnerability can be an analysis of the structure under a certain combination of static or dynamic loads, and the definition range is wider.

[0003] After long-term operation, cable-stayed bridges are prone to the phenomenon that components are damaged due to material property degradation or accidental events, which reduces the vulnerability performance of the cable-stayed bridge structure when encountering emergency events, and the vulnerability will evolve over time, showing time-varying characteristics. Analyzing the change of structural vulnerability in the time dimension is time-varying vulnerability. The current research on structural time-varying vulnerability mainly focuses on the change of seismic vulnerability over time, while the analysis of structural vulnerability under static loads is for a specific moment and cannot reflect the influence of time-varying factors on structural vulnerability. Therefore, it is urgent to carry out research.

[0004] Currently, the main methods for studying structural vulnerability are mainly divided into two categories: those based on energy flow and those based on geometric topology (structural configuration). The energy method is to find the important components of the structure through an energy network and evaluate the vulnerability of the structure, while the geometric topology method is to analyze the integrity and vulnerability of the structure through configuration. However, both of these two methods are difficult to evaluate the influence of time-varying factors on structural vulnerability, and at the same time, there are problems such as large computational amount, difficulty in considering the uncertainty of structural parameters and loads, and poor real-time performance, especially time-varying effects. At the same time, the research on structural time-varying vulnerability mainly focuses on the change of seismic vulnerability over time. The traditional process of time-varying seismic vulnerability analysis is as follows: First, select a degradation model that conforms to the actual situation, then conduct dynamic incremental analysis on the structures in different periods respectively to obtain the seismic vulnerability curves of the structures in different periods, and finally judge the influence of this time-varying characteristic on the seismic performance of the structure by comparing different vulnerability curves. However, this process cannot be used for the analysis of the vulnerability of structures under static loads or other forms of dynamic loads. Summary of the Invention

[0005] In view of this, the object of the present invention is to provide a time-varying vulnerability analysis method for cable-stayed bridges based on structural configuration and Bayesian networks, which is used to analyze the change of the vulnerability of the cable-stayed bridge system over time and serve as a reference for engineering safety evaluation.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A time-varying vulnerability analysis method for cable-stayed bridges based on structural configuration and Bayesian networks, comprising the following steps:

[0008] Step S1: Define the external load, the cable-stayed bridge system and each component as nodes of a variable structure discrete dynamic Bayesian network (Variable Discrete Dynamic Bayesian Networks, abbreviated as VDDBN), and pre-define the VDDBN topology;

[0009] Step S2: Considering the time-varying models and their uncertainties of the structural parameters and external loads, construct a VDDBN through parameter learning;

[0010] Step S3: Input evidence into the VDDBN to infer the posterior probabilities of all nodes in all time slices, and calculate the vulnerability probabilities of the components to establish the time-varying vulnerability curves of the components;

[0011] Step S4: Establish the time-varying vulnerability curve of the structure through clustering.

[0012] Further, the specific content of step S1 is as follows:

[0013] Step S11: Take the external load as the top-level parent node, and take the cable-stayed bridge system as the intermediate node and also the parent node of each component;

[0014] Step S12: Take each component as the bottom-level node, connect with the load and system nodes through directed arcs, and define the static network topology in a single time slice;

[0015] Step S13: Set that the load and system states in the next time slice are only related to the previous time slice, and different time slices are connected through the load and system nodes, that is, the directed arcs point from the load and system nodes in the previous time slice to the load and system nodes in the next time slice respectively, forming a transfer network topology;

[0016] Step S14: Divide the state of the load, system and component nodes to complete the definition of the VDDBN topology.

[0017] Further, the specific content of step S2 is as follows:

[0018] Step S21: Considering the time-varying effects and uncertainties of the structure and external loads, define the external loads and component properties as random variables subject to normal distribution. Meanwhile, determine the means and standard deviations of the uncertain parameter variables in each time slice within the dynamic network according to the time-varying models of the loads or component properties.

[0019] Step S22: Extract a number of parameter samples for all time slices through Monte Carlo sampling, and then input them into the finite element model of the cable-stayed bridge to calculate the strain energy of each component at different time slices. E i,j,t , thereby confirming the states of the components and system nodes and obtaining the parameter learning samples.

[0020] Step S23: Obtain the conditional probabilities between the VDDBN nodes through the learning samples to complete the construction of the VDDBN.

[0021] Further, the specific content of step S3 is as follows:

[0022] Step S31: Take the state of the load node in the first time slice as evidence and input it into the VDDBN to infer the state probabilities of all nodes at all time slices. Then sum up the state probabilities to obtain the probability that the component exceeds a certain dangerous state within different time slices, which is defined as the vulnerability overrun probability, and obtain the probability curve of the component exceeding the state at each time slice.

[0023] Step S32: Integrate the components of the cable-stayed bridge into the entire system using the clustering rule, and define the time-varying vulnerability curve of the system using the concepts of approximate series and approximate parallel.

[0024] Further, the vulnerability overrun probability is specifically:

[0025] (1)

[0026] The left side of equation (1) F represents the vulnerability overrun probability of component j at time t with respect to state s . The right side P is the state probability of component t at time s j,t represents the state of component j at time t . After obtaining the vulnerability overrun probabilities of the component at all times, the time point can be used as the abscissa and the probability obtained from equation (1) as the ordinate to establish the time-varying vulnerability curve of component j with respect to state s , representing the probability curve of component j exceeding state s at each time slice.

[0027] Specifically, the further step S4 is as follows:

[0028] Step S41: Disassemble the cable-stayed bridge structure into base clusters, and then take the curve with the largest vulnerable overrun probability in any base cluster as the time-varying vulnerability curve of the base cluster;

[0029] Step S42: Combine other components on the base cluster to form a new structure cluster. If the newly combined components are in series with the original structure cluster, take the curve with the largest vulnerable overrun probability as the time-varying vulnerability curve of the new structure cluster; if the newly combined components are in parallel with the original structure cluster, take the product of the vulnerable overrun probabilities of the components as the time-varying vulnerability curve of the new structure cluster;

[0030] Step S43: When the new structure cluster is the entire structural system, the obtained time-varying vulnerability curve is the time-varying vulnerability curve of the structure.

[0031] The present invention has the following beneficial effects compared with the prior art:

[0032] 1. The present invention takes into account the time-varying characteristics and uncertainties of external loads and component parameters;

[0033] 2. The present invention defines the failure probability of the system from the perspective of structural configuration, better considers the connection relationship between components, and avoids the cumbersome calculation of joint probability functions;

[0034] 3. The present invention only needs to obtain the observed data of some components to infer the vulnerability of all components and the system, and realizes the update of the time-varying vulnerability curve of the cable-stayed bridge under incomplete data. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is the flowchart of the method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0036] The present invention will be further described below with reference to the drawings and embodiments.

[0037] Please refer to Figure 1 , the present invention provides a time-varying vulnerability analysis method for cable-stayed bridges based on structural configuration and Bayesian network, including the following steps:

[0038] Step S1: Define the external load, the cable-stayed bridge system and each component as nodes of a variable structure discrete dynamic Bayesian network VDDBN, and pre-define the VDDBN topology;

[0039] Step S2: Consider the time-varying model and its uncertainty of structural parameters and external loads, and construct the VDDBN through parameter learning;

[0040] Step S3: Infer the posterior probabilities of all nodes in all time slices for the VDDBN input evidence, and calculate the component vulnerability probability to establish the time-varying vulnerability curve of the component;

[0041] Step S4: Establish the time-varying vulnerability curve of the structure through clustering.

[0042] In this embodiment, step S1 is specifically as follows:

[0043] Step S11: Take the external load as the top-level parent node, take the cable-stayed bridge system as the intermediate node (which is also the child node of the external load) and at the same time the parent node of each component;

[0044] Step S12: Take each component as the bottom-level node, connect it with the load and system nodes through directed arcs, and define the static network topology in a single time slice;

[0045] Step S13: Set that the load and system states in the next time slice are only related to the previous time slice, and different time slices are connected through the load and system nodes, that is, the directed arcs point from the load and system nodes in the previous time slice to the load and system nodes in the next time slice respectively, forming a transfer network topology;

[0046] Step S14: Divide the states of the load, system and component nodes to complete the definition of the VDDBN topology.

[0047] Preferably, in the state division of the node variables, according to each component E i,j,t ( i = 1, 2, …, n represents the number of samples, j = 1, 2, …, m represents the component number, t = 1, 2, … represents the time slice number) to divide the state of the component node s , and define the minimum value of the strain energy when the component with the maximum internal force yields E E as the most dangerous state of the component, and divide the component node state accordingly.

[0048] When E i,j,t is in the interval [0, γ 1 × E E ), the component is in a safe state ( s = 1);

[0049] When E i,j,t is in the interval γ 1 × E E , γ 2 ×E E ) When the component is in a slightly damaged state ( s = 2);

[0050] When E i,j,t is in the interval γ 2 × E E , γ 3 × E E ) the component is in a moderately damaged state ( s = 3);

[0051] When E i,j,t is in the interval γ 3 × E E , E E ) the component is in a severely damaged state ( s = 4);

[0052] When E i,j,t is in the interval E E , +∞), the component is in a failure state ( s = 5).

[0053] Then, calculate the sum of the strain energies of all components in the sample , and according to divide the states of the system nodes:

[0054] When is in the interval [0, μ 1 × m × E E ) the system is in a safe state ( s = 1);

[0055] When is in the interval μ 1 × m × E E , μ 2 × m × E E ) the system is in a slightly dangerous state ( s = 2);

[0056] When is in the interval μ 2 × m × E E, μ 3× m × E E ) When the system is in a moderately dangerous state ( s = 3);

[0057] When is in the interval μ 3× m × E E , m × E E ) the system is in a severely dangerous state ( s = 4);

[0058] When is in the interval m × E E , +∞), the system is in a damaged state ( s = 5).

[0059] Finally, the state of the load node variables is defined. The load node state is independent of the load magnitude and only related to the time slice. To simplify the analysis, the load node state of time slice 1 is defined as 1, the load node state of time slice 2 is defined as 2, and so on...

[0060] In this embodiment, step S2 is specifically as follows:

[0061] Step S21: Considering the time-varying effects and uncertainties of the structure and external loads, the external loads and component properties are respectively defined as random variables subject to normal distribution. At the same time, the means and standard deviations of the uncertain parameter variables of each time slice in the dynamic network are determined according to the time-varying models of the loads or component properties;

[0062] Step S22: Through Monte Carlo sampling, a number of parameter samples are drawn for all time slices, and then input into the finite element model of the cable-stayed bridge to calculate the strain energy of each component at different time slices E i,j,t , so as to confirm the states of the components and system nodes and obtain the parameter learning samples;

[0063] Step S23: Obtain the conditional probabilities between the VDDBN nodes through the learning samples to complete the construction of the VDDBN.

[0064] In this embodiment, step S3 is specifically as follows:

[0065] Step S31: Take the state of the first time - slice load node as evidence and input it into the VDDBN to infer the state probabilities of all nodes at all time - slices. Then sum up the state probabilities to obtain the probability that the component exceeds a certain dangerous state within different time - slices, which is defined as the vulnerability exceeding - limit probability, and obtain the probability curve of the component exceeding the state at each time - slice.

[0066] (1)

[0067] The left - hand side of Equation (1) F represents the vulnerability exceeding - limit probability of the component j at time t with respect to state s , and the right - hand side P is the state probability of being in different states at time t . After obtaining the vulnerability exceeding - limit probabilities of the component at all times, the time - varying vulnerability curve of the component with respect to state s j,t can be established with the time point as the abscissa and the probability obtained from Equation (1) as the ordinate, which represents the probability curve of the component j exceeding state t at each time - slice. j with respect to state s , and represents the probability curve of the component j exceeding state s at each time - slice.

[0068] Step S32: Integrate the components of the cable - stayed bridge into the whole system by using the clustering rule, and define the time - varying vulnerability curve of the system by using the concepts of approximate series and approximate parallel.

[0069] In this embodiment, Step S4 is specifically as follows:

[0070] Step S41: Disassemble the cable - stayed bridge structure into basic clusters, and then take the curve with the maximum vulnerability exceeding - limit probability in any basic cluster as the time - varying vulnerability curve of the basic cluster.

[0071] Step S42: Combine other components on the basic cluster to form a new structural cluster. If the newly combined component is in a series relationship with the original structural cluster (i.e., if the original structural cluster or the newly combined component fails, the new structural cluster also fails), then take the curve with the maximum vulnerability exceeding - limit probability as the time - varying vulnerability curve of the new structural cluster; if the newly combined component is in a parallel relationship with the original structural cluster (i.e., if the original structural cluster and the newly combined component fail simultaneously, the new structural cluster fails), then take the product of the vulnerability exceeding - limit probabilities of the components as the time - varying vulnerability curve of the new structural cluster.

[0072] Step S43: When the new structural cluster is the entire structural system, the obtained time - varying vulnerability curve is the time - varying vulnerability curve of the structure.

[0073] The above are only the preferred embodiments of the present invention, and all equivalent changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope of the present invention.

Claims

1. A time-varying vulnerability analysis method for cable-stayed bridges based on structural configuration and Bayesian network, characterized in that, It includes the following steps: Step S1: Define the external load, cable-stayed bridge system, and each component as nodes of a variable structure discrete dynamic Bayesian network (VDDBN), and pre-define the VDDBN topology; Step S2: Considering the time-varying models and their uncertainties of the structural parameters and external loads, construct the VDDBN through parameter learning; Step S3: Input evidence into the VDDBN to infer the posterior probabilities of all nodes in all time slices, and calculate the vulnerability probabilities of components to establish the time-varying vulnerability curves of components; Step S4: Establish the time-varying vulnerability curve of the structure through clustering; The specific content of step S2 is as follows: Step S21: Considering the time-varying effects and their uncertainties of the structure and external loads, define the external load and component attributes as random variables subject to normal distributions. At the same time, determine the means and standard deviations of the uncertain parameter variables in each time slice of the dynamic network according to the time-varying models of the loads or component attributes; Step S22: Extract a number of parameter samples for all time slices through Monte Carlo sampling, and then input them into the finite element model of the cable-stayed bridge to calculate the strain energy E of each component under different time slices i,j,t , thereby confirming the states of the components and system nodes to obtain parameter learning samples; Step S23: Obtain the conditional probabilities between the VDDBN nodes through learning samples to complete the construction of the VDDBN; The specific content of step S3 is as follows: Step S31: Input the state of the load node in the first time slice as evidence into the VDDBN to infer the state probabilities of all nodes in all time slices; then sum the state probabilities to obtain the probabilities of components exceeding a certain dangerous state in different time slices, defined as the vulnerable overrun probabilities, and obtain the probability curves of components exceeding the state in each time slice; Step S32: Use the clustering rules to integrate the components of the cable-stayed bridge into the entire system, and adopt the concepts of approximate series and approximate parallel to define the time-varying vulnerability curve of the system; The specific content of step S4 is as follows: Step S41: Decompose the cable-stayed bridge structure into basic clusters, and then take the curve with the maximum vulnerable overrun probability in any basic cluster as the time-varying vulnerability curve of the basic cluster; Step S42: Combine other components on the basic cluster to form a new structural cluster. If the newly combined components are in a series relationship with the original structural cluster, take the curve with the maximum vulnerable overrun probability as the time-varying vulnerability curve of the new structural cluster; if the newly combined components are in a parallel relationship with the original structural cluster, take the product of the vulnerable overrun probabilities of the components as the time-varying vulnerability curve of the new structural cluster; Step S43: When the new structural cluster is the entire structural system, the obtained time-varying vulnerability curve is the time-varying vulnerability curve of the structure.

2. The time-varying vulnerability analysis method of cable-stayed bridges based on structural configuration and Bayesian network according to claim 1, characterized in that The specific content of step S1 is as follows: Step S11: Take the external load as the top-level parent node, and take the cable-stayed bridge system as the intermediate node and also the parent node of each component; Step S12: Take each component as the bottom-level node, and connect it with the load and system nodes through directed arcs to define the static network topology in a single time slice; Step S13: Set that the load and system states in the next time slice are only related to the previous time slice, and connect different time slices through the load and system nodes, that is, the directed arcs point from the load and system nodes in the previous time slice to the load and system nodes in the next time slice respectively to form the transfer network topology; Step S14: Divide the state of the load, system, and component nodes to complete the definition of the VDDBN topology.

3. The time-varying vulnerability analysis method of cable-stayed bridges based on structural configuration and Bayesian network according to claim 1, characterized in that The vulnerable overrun probability is specifically: On the left side of the equal sign in Equation (1), F represents the vulnerability exceeding probability of component j at time t with respect to state s, and on the right side, P is the state probability in different states at time t; s j,t represents the state of component j at time t; After obtaining the vulnerability exceeding probability of the component at all times, with the time point as the abscissa and the probability obtained by formula (1) as the ordinate, a time-varying vulnerability curve of component j with respect to state s is established, which represents the probability curve of component j exceeding state s in each time slice.

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