DBN and Gamma distribution-based box girder bridge whole system performance degradation probability evaluation method

Abstract

The invention discloses a box girder bridge whole system performance degradation probability evaluation method based on DBN and Gamma distribution, and belongs to the technical field of box girder bridge performance degradation probability evaluation. Determining the staying time of each component of the box girder bridge; calculating related parameters of a Gamma distribution probability density function; calculating an accumulated probability density function and an accumulated survival probability function of each component of the box girder bridge; modeling performance reduction of the box girder bridge to obtain a transition probability; calculating state probability distribution of each component; a probability degradation curve of each component and the overall structure is formed through a dynamic Bayesian network; and evaluating the influence of the component on the probability degradation curve of the affiliated component and the overall structure. By adopting the DBN and Gamma distribution-based box girder bridge whole system performance degradation probability evaluation method, the performance degradation of the box girder bridge from components to parts and from the parts to the whole can be more scientifically predicted, so that the service life of the box girder bridge can be predicted from the probability level.

Description

Technical Field

[0001] The present invention relates to the technical field of performance degradation probability assessment of box girder bridges, and in particular to a method for assessing the performance degradation probability of the entire system of box girder bridges based on DBN and Gamma distribution. Background Art

[0002] As the core hub in the modern transportation network, the stability and safety of the structure of box girder bridges are the basis for ensuring smooth traffic. In the past forty years, approximately 80% of box girder bridges have been successively built, witnessing the rapid development of the national transportation infrastructure. However, over time, more than 430,000 box girder bridges have been in service for over 20 years, and problems such as aging and diseases have gradually emerged. Some box girder bridges are even facing severe situations such as insufficient bearing capacity. At the same time, the booming development of the transportation industry has led to a continuous increase in traffic loads, and the sharp growth in transportation demand has forced many box girder bridges to operate beyond their design life. This not only poses a huge test to the structural safety of box girder bridges themselves but also poses a potential threat to the stable operation of the entire transportation network. Therefore, attaching great importance to the aging problem of box girder bridges and strengthening their daily inspection and maintenance work are crucial for ensuring the safety and smoothness of the transportation network.

[0003] According to the "Specifications for Maintenance of Highway Bridges and Culverts" (JTGH11-2004), it is stipulated that "the regular inspection cycle is determined according to the technical condition, and the longest shall not exceed three years"; the newly revised "Specifications for Maintenance of Highway Bridges and Culverts" (JTG5120-2021) further clarifies that "for box girder bridges with a maintenance inspection status of Grade I, the regular inspection cycle shall not exceed 1 year; for box girder bridges with a maintenance inspection status of Grade II or III, the regular inspection cycle shall not exceed 3 years". Therefore, a huge amount of box girder bridge detection data is generated nationwide every year. How to accurately estimate the performance degradation degree of box girder bridges based on this detection information and effectively predict the degradation trend after maintenance intervention has become a key problem that urgently needs to be solved in the engineering field.

[0004] Currently, there are many performance evaluation and prediction models for box girder bridges. Methods such as reliability assessment based on physical models and Gamma curve degradation are usually only applicable to the analysis of individual components and lack reliable theoretical support when evaluating components and the overall structure. The neural network method based on data-driven has problems such as poor model interpretability and limited generalization ability; the analytic hierarchy process is greatly affected by subjective factors and it is difficult to quantify indicators; when analyzing the performance degradation of bridges using the semi-Markov method, the state sojourn time is often set as the Weibull distribution, and the distribution degradation analysis of components, parts, or the overall structure is carried out separately. However, this method has obvious drawbacks. If only based on the Weibull distribution degradation of components, it is difficult to reasonably infer the degradation distribution form of parts and the overall structure, and it is impossible to accurately grasp the degradation trend of bridge performance as a whole. Summary of the Invention

[0005] The object of the present invention is to provide a method for evaluating the probability of the overall system performance degradation of a box girder bridge based on DBN and Gamma distribution, starting from the analysis of components, and systematically solving the problems of evaluating and predicting the performance degradation of components, parts and the overall structure, as well as the influence of component replacement and maintenance on the performance degradation of the affiliated parts and the overall structure.

[0006] To achieve the above object, the present invention provides a method for evaluating the probability of the overall system performance degradation of a box girder bridge based on DBN and Gamma distribution, including the following steps: S1. Determine the composition of the box girder bridge; S2. Determine the sojourn time of each component of the box girder bridge; S3. Calculate the relevant parameters of the Gamma distribution probability density function based on the sojourn time of each component of the box girder bridge obtained in S2; S4. Calculate the cumulative probability density function and the cumulative survival probability function of each component of the box girder bridge through Monte Carlo simulation; S5. Model the performance degradation of the box girder bridge to obtain the transition probability; S6. Calculate the state probability distribution of each component based on the data obtained in S4; S7. According to the state probability distribution of each component obtained in S6, form the probability degradation curves of each part and the overall structure through a dynamic Bayesian network; S8. Evaluate the influence of components on the degradation curves of the affiliated parts and the overall structure.

[0007] Preferably, the specific operation of S1 is as follows: S11. The box girder bridge is composed of an upper structure, a lower structure and a deck system. The upper structure includes upper load-bearing components, upper general components and bearings. The lower structure includes slopes, abutments and pier foundations. The deck system includes deck pavement, expansion joint devices, guardrails and drainage systems; S12. Establish a topological structure containing circular nodes, line segments and connecting arrows to form a dynamic Bayesian network. The circular nodes represent the probabilities of the states of components, parts or the overall structure at a certain time point. The connecting arrows represent the transition probabilities between nodes. The two ends of the line segments have the same meaning. The topological structure is composed of a component layer, a part layer and an overall structure layer from bottom to top. The component layer is the observation layer, the part layer is the first hidden layer, and the overall structure layer is the second hidden layer.

[0008] Preferably, the specific operation of S2 is as follows: S21. Determine the composition weights of the component layer and the part layer in the topological structure in S12, and use them as the transition probabilities from the component layer to the part layer and from the part layer to the overall structure layer in the dynamic Bayesian network respectively. Divide the detection scores of the component layer in the topological structure into 5 score intervals, which respectively correspond to the 5 states of the component layer; S22. In S21, since the time value corresponding to the fifth scoring interval is infinite, only the first four scoring intervals are linearly fitted according to the detection scores. The endpoint score values ​​of the first four scoring intervals are respectively substituted into the linear scoring curves fitted by the first four scoring intervals, and the time points of the states corresponding to the endpoint score values ​​of the scoring intervals are extracted from the scoring curve. The residence time of each component in the component layer in each state is calculated according to the time points, as shown in formula (1): (1); in, Indicates status Length of stay, Indicates status The right end point of the stay time interval, Indicates status The right endpoint of the dwell time interval.

[0009] Preferably, the specific operation of S3 is: S31. Assume that the time that each component of the box girder bridge stays in each state is a random variable t , t Obeying the Gamma distribution, the state Depending on the length of stay t The probability density function of the change is formula (2), state The survival probability function is formula (4), the probability density function of Gamma distribution is formula (3), and formula (2), formula (3), and formula (4) are respectively expressed as: (2); (3); (4); Represents a random variable t The probability density function of represents the scale parameter of the probability density function of the Gamma distribution, represents the shape parameter of the probability density function of the Gamma distribution, represents the exponential function, represents the survival probability function; S32, by combining formula (5) and formula (6), the genetic algorithm is used to calculate the state The scale parameter of the Gamma distribution probability density function and shape parameters , formula (5) and formula (6) are expressed as: (5); (6); Among them, min represents minimization, represents time, represents the state of the average survival probability, represents the state of the sojourn time.

[0010] Preferably, the specific operation of S4 is as follows: S41. Denote the first 4 states as state 1, state 2, state 3, and state 4, and use Monte Carlo simulation to calculate the cumulative probability density functions of each component in the superstructure in state 1, state 1 to state 2, state 1 to state 3, and state 1 to state 4 , and similarly calculate the cumulative probability density functions of each component in the substructure and the bridge deck system in state 1, state 1 to state 2, state 1 to state 3, and state 1 to state 4 ; S42. Calculate the cumulative survival probability functions of each component in the superstructure in state 1, state 1 to state 2, state 1 to state 3, and state 1 to state 4 through the integral formula. Similarly, calculate the cumulative survival probability functions of each component in the substructure and the bridge deck system in state 1, state 1 to state 2, state 1 to state 3, and state 1 to state 4, where the integral formula is as shown in formula (7): (7); Among them, represents the cumulative survival probability function from state 1 to state ; represents the probability density function, represents the cumulative probability density function from state 1 to state .

[0011] Preferably, the specific operation of S5 is as follows: S51. Calculate the conditional probability of the box girder bridge: The performance of the box girder bridge deteriorates over time, and the state changes from low to high. The adjacent state transitions have Markov property, that is, the next state only depends on the current state and is independent of the past states. Therefore, the conditional probability expression of the box girder bridge is: (8); Among them, represents the conditional probability; represents when the state random variable; represents the specific value of the state random variable when; represents when the state random variable; represents the specific value of the state random variable when; represents Time state random variable; Indicates The specific value of the time state random variable; Indicates Time state random variable; Indicates The specific value of the time state random variable; Indicates that in the known All states before the time The conditional probability at the time; Indicates that in the known The state at the time The conditional probability at the time; S52. According to the Markov property of S51, a Markov chain is used to model the performance degradation of the box girder bridge in the state . In this model, considering the time series with a fixed time interval as the unit, at the next moment, that is, the box girder bridge with a fixed time unit interval from the current moment changes from the current state To another state The transition probability Is expressed by the conditional probability, see formula (9); when multiple states are transferred simultaneously, a transition probability matrix is formed, see formula (10); (9); (10); Among them, Indicates the transition probability from state To state , , Indicates the conditional probability, Indicates Row Column transition probability matrix, Indicates the total number of states, , .

[0012] Preferably, the specific operation of S6 is: taking the sojourn time Corresponding to the state As a random variable, then at , the box girder bridge at the next time step From state Transfer to the next adjacent state The probability is shown in formula (11), and the state probability distributions of the upper load-bearing members, upper general members and bearings are calculated using formula (12) to form a probability degradation curve. Formulas (11) and (12) are expressed as: (11); (12); Among them, represents the transition probability from state to state , represents the time step, represents the cumulative probability density function from state 1 to state , represents the state probability distribution of component in the th year, represents the state probability distribution of component in the th year, is the transition probability matrix, obtained by substituting formula (11) into formula (10), represents the time variable, is a vector. When , , representing the probability of the component being in each state at . At , the probability of being in state 1 is 1, and the probabilities of being in the other 4 states are all 0.

[0013] Preferably, the specific operation of S7 is as follows: S71. According to the state probability distributions of each component obtained in S6, use the dynamic Bayesian network to calculate the state probability distributions of the superstructure, substructure, and bridge deck system through formula (13), and form the probability degradation curves of each component. The expression of formula (13) is: (13); Among them, represents the state probability distribution curve of component , represents the probability that component transfers to component , q represents the total number of components included in the component; S72. According to the state probability distributions of each component obtained in S71, use the dynamic Bayesian network to calculate the state probability distribution of the overall structure through formula (14), and form the probability degradation curve of the overall structure. The expression of formula (14) is: (14); Among them, represents the state probability distribution curve of the overall structure, represents the state probability distribution curve of component , represents the probability that component transfers to the overall structure,r Indicates the total number of components included in the overall structure.

[0014] Preferably, the specific operation of S8 is as follows: at a specific service time of the box girder bridge, perform replacement or maintenance operations on one of the components, calculate the influence degree of the component on the probability degradation curves of the components to which it belongs and the overall structure respectively, and then evaluate its sensitivity to the overall structural performance.

[0015] By scientifically determining the composition weights of the components and components of the box girder bridge and using them as the transition probabilities from components to components and from components to the overall structure, the present invention breaks through the limitations of traditional single distribution forms and can more deeply and comprehensively reveal the underlying logic of bridge performance degradation; in addition, compared with the Weibull distribution, applying the Gamma distribution to describe the component state sojourn time has unique advantages.

[0016] From a theoretical perspective, the box girder bridge is a complex structural system, and there are close correlations between its components and components. The performance degradation of components does not occur in isolation, but will affect components through a certain transmission mechanism and then affect the overall structural performance. Using the composition weight as the transition probability from components to components and from components to the overall structure conforms to the basic principles of structural mechanics and systems engineering. In addition, compared with the Weibull distribution, the Gamma distribution has a more flexible form. In bridge structures, when components are affected by multiple factors acting together and the effects of these factors have a cumulative effect, the Gamma distribution can better describe its state sojourn time. Finally, in the case of noise or missing in bridge detection data, the parameter estimation of the Gamma distribution is less affected.

[0017] Therefore, the present invention adopts the above-mentioned probability evaluation method for the performance degradation of the entire system of the box girder bridge based on DBN and Gamma distribution, and has the following beneficial effects: (1) Through the probability evaluation method for the performance degradation of the box girder bridge, the present invention adopts the state scoring of the box girder bridge, based on the semi-Markov process of performance degradation of the dynamic Bayesian network (DBN) and Gamma distribution. The method is simple and operable, and can scientifically predict the performance degradation of the box girder bridge from components to components and from components to the whole, so as to predict the service life of the box girder bridge from the probability level; (2) It can predict the influence of the replacement or maintenance of components on the performance degradation trends of the components to which they belong and the overall structure, and provide a technical basis for the scientific maintenance and repair of the box girder bridge; (3) By performing separate Gamma distribution degradation analysis on the degradation of the bottom components, the performance degradation of each component can be understood more precisely, so as to more accurately evaluate the overall performance of the box girder bridge; (4) The prediction result is no longer a fixed value, but the probability of being in different states, which is more scientific and reasonable.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is the dynamic Bayesian network diagram of the present invention; Figure 2 is the cumulative probability density function diagram of the upper load-bearing member of the present invention; Figure 3 is the cumulative survival probability function diagram of the upper load-bearing member of the present invention; Figure 4 is the probability degradation curve diagram of the upper load-bearing member of the present invention; Figure 5 is the cumulative probability density function diagram of the upper general member of the present invention; Figure 6 is the cumulative survival probability function diagram of the upper general member of the present invention; Figure 7 is the probability degradation curve diagram of the upper general member of the present invention; Figure 8 is the cumulative probability density function diagram of the bearing of the present invention; Figure 9 is the cumulative survival probability function diagram of the bearing of the present invention; Figure 10 is the probability degradation curve diagram of the bearing of the present invention; Figure 11 is the probability degradation curve diagram of the upper structure of the present invention; Figure 12 is the probability degradation curve diagram of the lower structure of the present invention; Figure 13 is the probability degradation curve diagram of the bridge deck system of the present invention; Figure 14 is the probability degradation curve diagram of the overall structure of the box girder bridge of the present invention; Figure 15 is the probability degradation curve diagram of the bearing (after bearing replacement) of the present invention; Figure 16 is the probability degradation curve diagram of the upper structure (after bearing replacement) of the present invention; Figure 17 is the probability degradation curve diagram of the overall structure of the box girder bridge (after bearing replacement) of the present invention; Figure 18 is the probability degradation curve diagram of the upper load-bearing member (after reinforcement of the upper load-bearing member) of the present invention; Figure 19 is the probability degradation curve diagram of the upper structure (after reinforcement of the upper load-bearing member) of the present invention; Figure 20 It is the overall probability degradation curve of the box girder bridge after the upper load-bearing member is strengthened according to the present invention. Detailed implementation manners

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs.

[0022] Embodiment The present invention provides a method for evaluating the probability of performance degradation of the entire system of a box girder bridge based on DBN and Gamma distribution, including the following steps: S1. Determine the composition of the box girder bridge. The specific operation is as follows: S11. The box girder bridge is composed of an upper structure, a lower structure, and a bridge deck system. The upper structure includes an upper load-bearing member, an upper general member, and a bearing. The lower structure includes a slope protection, an abutment, and a pier foundation. The bridge deck system includes a bridge deck pavement, an expansion joint device, a guardrail, and a drainage system.

[0023] S12. Establish a topological structure containing circular nodes, line segments, and connection arrows to form a dynamic Bayesian network. The circular nodes represent the probabilities of the states of components, parts, or the overall structure at a certain time point. The connection arrows represent the transition probabilities between nodes. The two ends of the line segment represent the same meaning. The topological structure is divided into a component layer, a part layer, and an overall structure layer from bottom to top. The component layer is the observation layer, the part layer is the first hidden layer, and the overall structure layer is the second hidden layer.

[0024] Among them, the formed dynamic Bayesian network is as Figure 1 shown; in the figure represents the time step, represents the state probability of the overall structure at the th moment, represents the state probability of the overall structure at the moment of, represents the state probability of the overall structure at the moment of, represents the state probability of the 0th part at the moment of, represents the state probability of the 0th part at the moment of, represents the state probability of the 0th part at the moment of, represents the th part at the moment of, represents the The state probability of a component at time , indicating the state probability of the th component at time , indicating the state probability of the 0th component at time , indicating the state probability of the 0th component at time , indicating the state probability of the 0th component at time , indicating the th component at time , indicating the th component at time , indicating the th component at time .

[0025] S2. Determine the sojourn time of each component of the box girder bridge. The specific operation is as follows: S21. Refer to the "Technical Condition Assessment Standard for Highway Bridges (JTG / T H21—2011)" to determine the composition weights of the component layer and the component layer in the topological structure in S12, which are used as the transition probabilities from the component layer to the component layer and from the component layer to the overall structure layer in the dynamic Bayesian network respectively. Divide the detection scores of the component layer in the topological structure obtained from the road network company into 5 scoring intervals, and classify them into 1-5 categories according to the standards of functional integrity, minor damage, moderate damage, severe damage to serious damage, corresponding to the 5 states of the component layer respectively, as shown in Table 1.

[0026] Table 1 Classification boundaries of the component layer states of the box girder bridge ;

[0027] S22. In S21, since the time value corresponding to the 5th scoring interval can be infinite, only the first 4 scoring intervals are linearly fitted according to the detection scores. Substitute the end-point scores of the first 4 scoring intervals into the linear scoring curves fitted for the first 4 scoring intervals respectively, and extract the time points of the states corresponding to the end-point scores of the scoring intervals from the scoring curves. Calculate the sojourn time of each component of the component layer in each state according to the time points, as shown in formula (1): (1); where represents the sojourn time of state , represents the right end point of the sojourn time interval of state , represents state The right endpoint of the dwell time interval.

[0028] For the upper load-bearing components, the residence time of the first four states is calculated according to formula (1): t 1 =9 years, t 2 =14 years, t 3 =20 years and t 4 = 25 years. The residence time of other components is detailed in Table 2.

[0029] Table 2 The residence time of each component in different states of box girder bridge ;

[0030] S3, calculate the relevant parameters of the Gamma distribution probability density function through the residence time of each component of the box girder bridge obtained in S2, and the specific operation is: S31. Assume that the time that each component of the box girder bridge stays in each state is a random variable t , t Obeying the Gamma distribution, the state Depending on the length of stay t The probability density function of the change is formula (2), state The survival probability function is formula (4), the probability density function of the Gamma distribution is formula (3), and formula (2), formula (3), and formula (4) are respectively expressed as: (2); (3); (4); Represents a random variable t The probability density function of represents the scale parameter of the probability density function of the Gamma distribution, represents the shape parameter of the probability density function of the Gamma distribution, represents the exponential function, represents the survival probability function.

[0031] S32, by combining formula (5) and formula (6), the genetic algorithm is used to calculate the state The scale parameter of the Gamma distribution probability density function and shape parameters , formula (5) and formula (6) are expressed as: (5); (6); where min represents minimization, represents time, represents the state of the average survival probability, represents the state of the sojourn time.

[0032] S4. Calculate the cumulative sojourn time and cumulative survival probability function of each component of the box girder bridge through Monte Carlo simulation. The specific operation is as follows: S4. Calculate the cumulative probability density function and cumulative survival probability function of each component of the box girder bridge through Monte Carlo simulation. The specific operation is as follows: S41. Denote the first 4 states as state 1, state 2, state 3, and state 4, and use Monte Carlo simulation to calculate the cumulative probability density functions of each component in the superstructure in state 1, state 1 to state 2, state 1 to state 3, and state 1 to state 4 , and the cumulative probability density function curves of the upper load-bearing components, upper general components, and bearings are as Figure 2 , Figure 5 , Figure 8 shown. It can be seen from Figure 2 that as the number of states increases, the variance of the cumulative probability density function of the upper load-bearing components becomes larger, and the cumulative probability density function from state 1 to state 4 reaches the maximum at 69 years; it can be seen from Figure 5 that compared with the upper load-bearing components, the time corresponding to the peak value of the cumulative probability density function of the upper general components is smaller, and the cumulative probability density function from state 1 to state 4 reaches the maximum at 36 years; it can be seen from Figure 8 that compared with the upper load-bearing components and upper general components, the time corresponding to the peak value of the cumulative probability density function of the bearings is the smallest, and the cumulative probability density function from state 1 to state 4 reaches the maximum at 22 years. Similarly, the cumulative probability density functions of each component in the lower structure and deck system in state 1, state 1 to state 2, state 1 to state 3, and state 1 to state 4 can be calculated .

[0033] S42. Calculate the cumulative survival probability functions of each component in the superstructure in state 1, state 1 to state 2, state 1 to state 3, and state 1 to state 4 through the integral formula (7). The images of the cumulative survival probability functions of the upper load-bearing components, upper general components, and bearings are as Figure 3 , Figure 6 , Figure 9 shown. It can be seen from Figure 3It can be seen that the downward trends of all four curves are first slow, then rapid, and finally become slow again. Moreover, with the increase of the cumulative state, the downward trend gradually slows down. The time corresponding to the average survival probability (the survival probability function value is 50%) for the first four cumulative states is 68 years, and the survival probability drops to 0 at 120 years. Figure 6 、 Figure 9 The downward trend of the curve is similar to that of Figure 3 . Among them, Figure 6 shows that when the cumulative survival probability of the upper general components drops to 0 in the first four states, the time is 80 years, 40 years less than that of the upper load-bearing components; Figure 9 In (7); where, represents the cumulative survival probability function from state 1 to state ; represents the probability density function, represents the cumulative probability density function from state 1 to state .

[0034] S5. Model the performance degradation of the box girder bridge to obtain the transition probability. The specific operation is as follows: S51. Calculate the conditional probability of the box girder bridge: The performance of the box girder bridge will degrade over time, that is, the state of the box girder bridge will change from low to high. The transition between adjacent states has the Markov property, that is, the box girder bridge being in the next state is only related to the current state and has nothing to do with the past state. Therefore, the conditional probability expression of the box girder bridge is: (8); where, represents the conditional probability; represents the state random variable at ; represents the specific value of the state random variable at ; represents the state random variable at ; represents the state random variable at ; represents the specific value of the state random variable at ; represents denote the specific value of the state random variable at denote that at known all previous states the conditional probability at time denote that at known the state at the conditional probability at

[0035] S52. According to the Markov property of S51, a Markov chain is used to model the performance degradation of the box girder bridge in state . In this model, considering a time series with a fixed time interval as the unit, the transition probability that the box girder bridge at the next moment (i.e., one fixed time unit interval from the current moment) changes from the current state to another state can be expressed by the conditional probability, as shown in formula (9); when multiple states transfer simultaneously, a transition probability matrix is formed, as shown in formula (10); (9); (10); where denotes the transition probability from state to state , , denotes the conditional probability, denotes the transition probability matrix ( rows columns), denotes the total number of states, , .

[0036] S6. Calculate the state probability distribution of each component through the data obtained in S4. The specific operation is as follows: Take the sojourn time corresponding to state as a random variable. Then, at , the probability that the box girder bridge transfers from state to the next adjacent state at the next time step is shown in formula (11). Use formula (12) to calculate the state probability distributions of the upper load-bearing components, upper general components, and bearings, and form a probability degradation curve. The probability degradation curves of the upper load-bearing components, upper general components, and bearings are as shown in Figure 4 , Figure 7 , Figure 10 .

[0037] Compare Figure 4 , Figure 7 withFigure 10 It can be found that three types of components, namely the upper load-bearing component, the upper general component, and the support, all gradually change from a low state to a high state over time, and the peak probabilities of states 1 to 4 decrease step by step. At any moment, the sum of the probabilities of all states is always 1; Figure 4 The upper load-bearing component starts to enter state 5 at the 40th year and fully enters state 5 at the 120th year; Figure 7 The upper general component starts to enter state 5 at the 18th year and fully enters state 5 at the 80th year; Figure 10 The middle support starts to enter state 5 at the 12th year and fully enters state 5 at the 47th year. Formulas (11) and (12) are expressed as: (11); (12); Among them, represents the transition probability from state to state , represents the time step, represents the cumulative probability density function from state 1 to state , represents the state probability distribution of component u in the th year, represents the state probability distribution of component in the th year, is the transition probability matrix, which can be obtained by substituting formula (11) into formula (10), represents the time variable, is a vector. When , , which represents the probability of the component being in each state at . At , the probability of being in state 1 is 1, and the probabilities of being in the other four states are all 0.

[0038] S7. According to the state probability distributions of each component obtained in S6, a probability degradation curve is formed through a dynamic Bayesian network. The specific operation is as follows: S71. According to the state probability distributions of each component obtained in S6, the state probability distributions of the superstructure, substructure, and bridge deck system are calculated through a dynamic Bayesian network using formula (13) to form the probability degradation curves of each component. The probability degradation curves of the superstructure, substructure, and bridge deck system are respectively as Figure 11 , Figure 12 , Figure 13 shown. By comparing Figure 11 , Figure 12 andFigure 13 It can be seen that the curve laws of the three figures have both similarities and differences. The similarities are as follows: over time, the peak probabilities from state 1 to state 4 decrease step by step; at any point in time, the sum of the probabilities of each state is always 1; the maximum probabilities of state 1 and state 5 are both 1. The differences are as follows: Figure 11 In [reference], the smoothness of the curves of state 4 and state 5 is slightly inferior to that of state 1 and state 2. The superstructure generally enters state 5 in the 70th year and completely enters state 5 in the 120th year. Figure 12 In [reference], the curves of state 3, state 4, and state 5 of the substructure are smoother than the corresponding state curves in Figure 11 and Figure 13 . The speed of entering state 5 is relatively slow in the first 60 years and then speeds up, and it completely enters state 5 in the 120th year. Figure 13 In [reference], the peak decline gradients of state 3, state 4, and state 5 are the largest, and the peak of state 4 is severely left - skewed. After entering state 5, the rising speed is relatively fast in the early stage and then slows down, and it completely enters state 5 in the 50th year. The expression of formula (13) is: (13); Among them, represents the state probability distribution curve of component , represents the probability that component transfers to component , q represents the total number of components included in the part; the transfer probability is obtained through Table 3: Table 3 Weight values (transfer probabilities) of each component of the box - girder bridge ;

[0039] S72. According to the state probability distributions of each component obtained in S71, the state probability distribution of the overall structure is calculated by using formula (14) through a dynamic Bayesian network, forming the overall structure probability degradation curve, as shown in Figure 14 . It can be seen from the figure that after the overall structure enters state 3, the probability rising trend is relatively slow between the 9th year and the 18th year; the probability rise of state 4 also slows down between the 10th year and the 38th year; the probability of state 5 shows a relatively slow rising trend between the 20th year and the 61st year. This indicates that the overall degradation law of the bridge structure is: the degradation is relatively fast in the short term in the early stage, relatively slow in the long term in the middle stage, and relatively fast again in the relatively long term in the later stage. At the 72nd year, the bridge has a 50% probability of entering the severely damaged state (state 5). It can be inferred that the average life of the bridge is about 72 years, and there is only a probability of less than 10% to survive to 100 years. The expression of formula (14) is: (14); Among them, Represents the state probability distribution curve of the overall structure, Represents the component State probability distribution curve of, Represents the component Probability of transferring to the overall structure, r Represents the total number of components included in the overall structure. The transfer probabilities are shown in Table 4: Table 4 Weights (transfer probabilities) of components of box girder bridge ;

[0040] S8. Evaluate the influence of each component on the probability degradation curve. The specific operation is as follows: At a specific service time of the box girder bridge, replace or repair one of the components, and calculate the influence degree of the component on the probability degradation curves of the component it belongs to and the overall structure respectively, so as to evaluate its sensitivity to the performance of the overall structure.

[0041] Hypothesis 1: Assume that the bearings of the box girder bridge are replaced with new bearings in the 15th year. Therefore, the bearings are degraded again after the 15th year. The probability degradation curve of the bearings after re - degradation is as Figure 15 shown. It can be seen from the figure that the bearings are completely degraded in the 60th year after re - degradation; Using the dynamic Bayesian network, the probability degradation curve of the superstructure after bearing replacement is as Figure 16 shown. Comparing Figure 11 with Figure 16 it can be known that the probability of the superstructure being in state 1 has increased to some extent. However, the increase in its duration is not significant; at the same time, the time when the probability of the superstructure being in state 2 decreases is postponed, but the duration of this state does not increase significantly either; generally speaking, in the time period from the 15th year to the 60th year after bearing replacement, the state of the superstructure has been improved to a certain extent, but the effect is not very obvious. In addition, since the bearings are completely degraded after the 60th year and can no longer affect the performance of the superstructure, starting from the 60th year, the superstructure will continue to develop according to its original degradation curve.

[0042] Using the dynamic Bayesian network, the probability degradation curve of the overall structure after bearing replacement is as Figure 17 shown. Comparing Figure 17 with Figure 14 it is found that except for slight fluctuations in states 1 and 2 in the 15th year, states 3 to 5 hardly change; from the perspective of the transfer of structural performance, since the probability of the performance state of the bearings transferring to the superstructure is small, and the probability of transferring from the superstructure to the overall structure is even smaller, the measure of bearing replacement has little effect on improving the performance of the overall structure.

[0043] Hypothesis 2: Assume that the technical performance indicators of the upper load-bearing members decline due to the gradual aging of the materials over time. To improve their condition, reinforcement and repair are carried out on them in the 60th year of the structure's service life. Assume that the condition of the upper load-bearing members after reinforcement and repair returns to 70% of the condition of a new bridge. The probability degradation curve of the upper load-bearing members after reinforcement is as shown in Figure 18 shown. By comparing Figure 18 with Figure 4 , it can be seen that only the states from state 2 to state 5 of the members change in the 60th year. In the 115th year, there is a 50% probability that the members enter state 5, and the time point of their complete degradation is the 157th year. Compared with before the repair, its service life is extended by 37 years.

[0044] Using the dynamic Bayesian network, the probability degradation curve of the state of the upper load-bearing members after reinforcement is as shown in Figure 19 shown. It can be seen from the figure that in the 60th year, significant mutations occur in states 2 to 5, and their mutation values are 0.426, 0.138, -0.486, and -0.081 respectively. This result shows that after the upper load-bearing members are reinforced and repaired, it has a significant improvement effect on the state of the upper structure and effectively improves the performance of the structure.

[0045] Further analyze the state of the overall structure after the upper load-bearing members are reinforced through the dynamic Bayesian network. Its probability degradation curve is as shown in Figure 20 shown. By comparing Figure 20 with Figure 14 , it is found that in the 60th year, the probability degradation curve of the overall structure being in state 2 rises significantly, the probability value of being in state 3 first decreases and then slightly rebounds, the probability curve of being in state 4 decreases significantly, and the probability of being in state 5 decreases slightly. In addition, the time point corresponding to the probability value of 50% in the state 5 curve is postponed from the original 71st year to the 81st year, and the average life of the structure increases by 10 years. The above analysis results fully illustrate that implementing reinforcement and repair measures on the upper load-bearing members can significantly extend the service life of the overall bridge and improve the durability and reliability of the bridge structure.

[0046] Similarly, based on the Markov theory and with the help of the dynamic Bayesian network, it is possible to deeply analyze the improvement of the state of other components and their affiliated components and the overall bridge structure after replacement or repair operations, thereby providing a scientific basis for the maintenance and management of the bridge structure.

[0047] Therefore, by adopting the above-mentioned probability assessment method for the overall system performance degradation of box girder bridges based on DBN and Gamma distribution, the present invention can more scientifically predict the performance degradation of box girder bridges from components to parts and from parts to the whole, and thus predict the service life of box girder bridges from the probability level.

[0048] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements do not enable the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. Probability assessment method for the overall system performance degradation of box girder bridges based on DBN and Gamma distribution, characterized in that: It includes the following steps: S1. Determine the composition of the box girder bridge; S2. Determine the sojourn time of each component of the box girder bridge; S3. Calculate the relevant parameters of the Gamma distribution probability density function based on the sojourn time of each component of the box girder bridge obtained in S2; S4. Calculate the cumulative probability density function and cumulative survival probability function of each component of the box girder bridge through Monte Carlo simulation; S5. Model the performance degradation of the box girder bridge to obtain the transition probability; S6. Calculate the state probability distribution of each component based on the data obtained in S4; S7. According to the state probability distribution of each component obtained in S6, form the probability degradation curves of each component and the overall structure through a dynamic Bayesian network; S8. Evaluate the influence of components on the degradation curves of their respective components and the overall structure.

2. The probability assessment method for the overall system performance degradation of a box girder bridge based on DBN and Gamma distribution according to claim 1, wherein: The specific operation of S1 is as follows: S11. The box girder bridge consists of an upper structure, a lower structure, and a deck system. The upper structure includes upper load-bearing components, upper general components, and bearings. The lower structure includes slopes, abutments, and pier and abutment foundations. The deck system includes deck pavement, expansion joint devices, guardrails, and drainage systems; S12. Establish a topological structure containing circular nodes, line segments, and connection arrows to form a dynamic Bayesian network. Among them, the circular nodes represent the probabilities of each state of the components, parts, or the overall structure at a certain time point. The connection arrows represent the transition probabilities between nodes. The two ends of the line segments have the same meaning. The topological structure is divided into a component layer, a part layer, and an overall structure layer from bottom to top. The component layer is the observation layer, the part layer is the first hidden layer, and the overall structure layer is the second hidden layer.

3. The probability assessment method for the overall system performance degradation of box girder bridges based on DBN and Gamma distribution according to claim 2, characterized in that: The specific operation of S2 is as follows: S21. Determine the composition weights of the component layer and the part layer in the topological structure in S12, which are used as the transition probabilities from the component layer to the part layer and from the part layer to the overall structure layer in the dynamic Bayesian network. Divide the detection scores of the component layer in the topological structure into 5 score intervals, which correspond to 5 states of the component layer respectively; S22. In S21, since the time value corresponding to the 5th score interval is infinite, only the first 4 score intervals are linearly fitted according to the detection scores. Substitute the end-point score values of the first 4 score intervals into the linear score curves fitted for the first 4 score intervals respectively, and extract the time points of the states corresponding to the end-point score values of the score intervals from the score curves. Calculate the sojourn time of each component in each state of the component layer according to the time points, as shown in formula (1): (1)； Among them, represents the sojourn time of the state represents the right endpoint of the sojourn time interval represents the right endpoint of the sojourn time interval 4. The method for evaluating the probability of the overall system performance degradation of a box girder bridge based on DBN and Gamma distribution according to claim 3, characterized in that: The specific operation of S3 is as follows: S31. Let the sojourn time of each component of the box girder bridge in each state be a random variable t , t which follows a Gamma distribution. Then the probability density function of state changing with the sojourn time t is given by Equation (2), the survival probability function of state is given by Equation (4), and the probability density function of the Gamma distribution is given by Equation (3). Equations (2), (3), and (4) are respectively expressed as follows: (2)； (3)； (4)； represents a random variable t of the probability density function represents the scale parameter of the probability density function of the Gamma distribution represents the shape parameter of the probability density function of the Gamma distribution represents the exponential function represents the survival probability function S32, by combining formula (5) and formula (6), the genetic algorithm is used to calculate the state The scale parameter of the Gamma distribution probability density function and shape parameters , formula (5) and formula (6) are expressed as: (5)； (6)； where min represents minimization, represents time, represents the state of the average survival probability, represents the state of the sojourn time.

5. The method for evaluating the probability of the overall system performance degradation of a box girder bridge based on DBN and Gamma distribution according to claim 4, wherein: The specific operation of S4 is as follows: S41. Denote the first four states as State 1, State 2, State 3, and State 4, and use Monte Carlo simulation to calculate the cumulative probability density functions of each component in the superstructure at State 1, from State 1 to State 2, from State 1 to State 3, and from State 1 to State 4. Similarly, calculate the cumulative probability density functions of each component in the substructure and the bridge deck system at State 1, from State 1 to State 2, from State 1 to State 3, and from State 1 to State 4. ; S42. Calculate the cumulative survival probability functions of each component of the upper structure in state 1, from state 1 to state 2, from state 1 to state 3, and from state 1 to state 4 through the integral formula. Similarly, calculate the cumulative survival probability functions of each component of the lower structure and the deck system in state 1, from state 1 to state 2, from state 1 to state 3, and from state 1 to state 4. The integral formula is shown in formula (7): (7)； Among them, represents the cumulative survival probability function from state 1 to state ; represents the probability density function, represents the cumulative probability density function from state 1 to state .

6. The probability assessment method for the overall system performance degradation of box girder bridges based on DBN and Gamma distribution according to claim 5, wherein: The specific operation of S5 is as follows: S51. Calculate the conditional probability of the box girder bridge: The performance of the box girder bridge degrades over time, and the state changes from low to high. The adjacent state transitions have Markov property, that is, the next state only depends on the current state and is independent of the past states. Therefore, the conditional probability expression of the box girder bridge is: (8)； Among them, represents the conditional probability; represents the state random variable at time represents the specific value of the state random variable at time represents the state random variable at time represents the specific value of the state random variable at time represents the state random variable at time represents the specific value of the state random variable at time represents the state random variable at time represents the specific value of the state random variable at time represents the conditional probability at time given all the previous states at time ; represents the conditional probability at time given the state at time ; S52. According to the Markov property of S51, a Markov chain is used to model the performance degradation of the box girder bridge in the state i . In this model, considering a time series with a fixed time interval as the unit, at the next moment, that is, after a fixed time unit from the current moment, the box girder bridge in the current state transitions to another state . The transition probability is expressed by conditional probability, as shown in Equation (9); when multiple states transition simultaneously, a transition probability matrix is formed, as shown in Equation (10). (9)； (10)； Among them, represents the transition probability from state to state . , represents the conditional probability, represents the transition probability matrix of the row and column.

7. The method for evaluating the probability of the overall system performance degradation of a box girder bridge based on DBN and Gamma distribution according to claim 6, wherein: The specific operation of S6 is as follows: the sojourn time corresponding to is used as a random variable. Then, at , the probability that the box girder bridge transfers from the state to the next adjacent state at the next time step is shown in Formula (11). The state probability distributions of the upper load-bearing members, upper general members, and bearings are calculated using Formula (12) to form a probability degradation curve. Formulas (11) and (12) are expressed as: (11)； (12)； Among them, represents the transition probability from state to state . represents the time step, represents the cumulative probability density function from state 1 to state . represents the state probability distribution of component in the th year. represents the state probability distribution of component in the th year. is the transition probability matrix, obtained by substituting formula (11) into formula (10). represents the time variable, is a vector. When , , representing the probability of the component being in each state at . At , the probability of being in state 1 is 1, and the probabilities of being in the other 4 states are all 0.

8. The method for evaluating the probability of the overall system performance degradation of a box girder bridge based on DBN and Gamma distribution according to claim 7, characterized in that: The specific operation of S7 is as follows: S71. Based on the state probability distributions of each component obtained in S6, use the dynamic Bayesian network to calculate the state probability distributions of the superstructure, substructure, and bridge deck system through formula (13), and form the probability degradation curves of each component. The expression of formula (13) is as follows: (13)； Among them, represents the state probability distribution curve of the component , represents the probability that the component transfers to the component , q represents the total number of components included in the component; S72. Based on the state probability distributions of each component obtained in S71, use the dynamic Bayesian network to calculate the state probability distribution of the overall structure through formula (14), and form the probability degradation curve of the overall structure. The expression of formula (14) is as follows: (14)； Among them, represents the state probability distribution curve of the overall structure, represents the component 's state probability distribution curve, represents the probability that the component transfers to the overall structure, r represents the total number of components included in the overall structure.

9. The method for evaluating the probability of the overall system performance degradation of a box girder bridge based on DBN and Gamma distribution according to claim 8, wherein: The specific operation of S8 is as follows: At a specific service time of the box girder bridge, perform replacement or repair operations on one of the components, calculate the influence degrees of the component on the probability degradation curves of the component to which it belongs and the overall structure respectively, and then evaluate its sensitivity to the performance of the overall structure.

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