Bridge structure risk early warning method based on Bayesian decision and information value

Abstract

The invention provides a bridge structure risk early warning method based on Bayesian decision and information value. According to the method, Bayesian prior analysis is carried out through structure monitoring data, a cost model comprises structure failure cost, maintenance cost and management and control cost, and a structure state model is obtained through structure fatigue reliability analysis. Bayesian prognosis test analysis is carried out in the next step, short-term future monitoring data distribution is predicted based on current monitoring data, then structural fatigue reliability analysis is carried out on the possibility of each kind of monitoring data, corresponding failure risk indexes are calculated, and information values are calculated based on a cost model. And finally, through maximizing the information value, obtaining an optimal structure early warning threshold value under Bayesian prognosis test analysis so as to determine the optimal early warning time. According to the self-adaptive structure risk early warning method, the early warning cost and the structure performance degradation are comprehensively considered, and rapid early warning decisions with safety guarantee and economic benefits can be achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of civil engineering, and particularly relates to a bridge structure risk early warning method based on Bayesian decision-making and information value. Background Art

[0002] Bridges are an indispensable part of the transportation network, ensuring smooth connections between regions and the continuity of economic activities. During their service life, the structural performance of bridges gradually degrades. An early warning system can detect potential risks in the structure in advance, issue alarms in a timely manner, prevent potential accidents, and ensure the safety of people's lives and property. At the same time, by continuously monitoring the health status of bridges, such a system can help relevant departments formulate more scientific maintenance and repair plans, avoid long-term traffic interruptions caused by sudden failures, and thus improve the efficiency and reliability of public services. Therefore, it is very important to ensure the safe operation of bridges and quickly and accurately warn of potential safety risks that bridges may suffer.

[0003] Traditional methods usually involve over-limit alarms for a single indicator, and corresponding early warning decisions are made only when a monitored indicator exceeds a pre-set early warning threshold. This single threshold setting does not fully consider the actual situation of bridges under different working conditions. Since bridges are affected by the coupled action of various environmental factors such as strong winds, temperature changes, and vehicle loads, over-limit alarms for a single indicator may not accurately reflect the true safety status of the bridge. At the same time, existing bridge early warning methods are mostly static early warnings, that is, the early warning thresholds are often set as constants based on design parameters in the initial stage of bridge construction, without considering the structural effect changes or structural performance degradation caused by various environmental actions and making corrections. This may result in the early warning system failing to issue an alarm in a timely manner (false negative) when there are already significant safety hazards in the bridge, or triggering an alarm (false positive) due to a short-term failure of the sensor or interference during data transmission, resulting in abnormal data. On the other hand, existing early warning methods do not systematically consider the costs incurred by early warning actions. Relying solely on over-limit alarms for a single indicator may lead to frequent false positives and false negatives, resulting in a large waste of manpower, material resources, and economic losses. Therefore, systematically considering the cost-benefit of bridge early warning is conducive to the long-term support and sustainable development of the bridge structure early warning system, thus ensuring the long-term safe operation of the bridge. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems in the prior art, and a bridge structure risk early warning method based on Bayesian decision-making and information value is proposed. The method is applicable to early warning of potential risks to the structure based on monitoring data.

[0005] The present invention is realized through the following technical solutions. The present invention provides a bridge structure risk early warning method based on Bayesian decision-making and information value. The method includes the following steps:

[0006] Step 1, perform Bayesian prior analysis: According to the Bayesian prior analysis theory, construct corresponding cost models and structural state probability models. The cost models include structural failure costs, structural maintenance costs, and structural operation costs. The structural state probability model is obtained through fatigue reliability analysis based on crack propagation, and then based on the maximum expected utility theory, the most preferred prior decision and the corresponding prior analysis cost under the currently available monitoring data are obtained.

[0007] Step 2, perform Bayesian pre-posterior analysis: Based on the current monitoring data, predict the future short-term monitoring data distribution. For each possibility of the monitoring data, perform posterior analysis, and then based on the maximum expected utility theory, obtain the optimal decision and posterior analysis cost under each possibility of the monitoring data. The cost models used are the same as those in Step 1, and the structural state probability model used is obtained by updating the structural state probability model in Step 1 through monitoring data and Bayesian theory.

[0008] Step 3, calculate the information value: According to the future short-term monitoring data distribution predicted in Step 2, calculate the mathematical expectation of the difference between the posterior analysis cost and the prior analysis obtained under each possibility of the monitoring data to obtain the information value. Then, by maximizing the information value, obtain the optimal early warning threshold under Bayesian pre-posterior analysis, which can ensure the maximum expected utility under the future monitoring data distribution.

[0009] Step 4, conduct bridge structure early warning: According to the structural reliability index, failure probability, and failure risk function obtained through fatigue reliability analysis, and the optimal early warning threshold obtained through information value analysis, conduct early warning judgment. When the failure risk function value in a certain time period is higher than the optimal early warning threshold, issue an early warning in the previous time period.

[0010] Further, the specific construction of the cost model in Step 1 is as follows: The cost model includes structural failure cost C F , structural maintenance cost C R , and structural operation cost C O . The structural failure cost includes the direct cost related to structural damage and the indirect cost caused by the loss of structural function. The structural maintenance cost includes the human and material costs required for maintenance and the indirect cost caused by structural maintenance. The structural operation cost includes the economic loss cost caused by control measures. The calculation methods of the structural failure cost C F and the structural maintenance cost C R are shown in the following formula:

[0011]

[0012] Among them represents the economic loss caused by structural failure is the cost required for a single repair of the structure, r is the discount rate, and t w represents the time of early warning; the operating cost C O can be calculated according to the specific structure and scenario

[0013] Furthermore, in step one, the structural state probability model is specifically modeled as follows: based on the fatigue crack growth theory, the structural fatigue reliability is analyzed to obtain the structural reliability index and failure probability within a certain future time; the relevant formulas of the fatigue crack growth theory are as follows

[0014]

[0015]

[0016] Among them, a represents the fatigue crack depth; n represents the number of cycles of the fatigue load; a(n) represents the fatigue crack depth at the nth cycle of the fatigue load; C m and m are both fatigue crack growth constants, which can be determined through material tests; G is the crack geometry correction factor; Δσ is the equivalent fatigue stress amplitude; for the convenience of fatigue reliability analysis, it is assumed that the value of the geometry correction factor is a constant 1, and thus the following formula can be obtained by integration

[0017]

[0018] Among them, a0 represents the initial fatigue crack depth; v represents the mean value of the number of load cycles, which can be determined according to the preset time interval; a(t) represents the fatigue crack depth at time t; the fatigue limit state equation can be defined as

[0019] g(t) = a th - a(t)

[0020] Among them, a th is the limit threshold of the fatigue crack; the HL - RF algorithm is used to solve the fatigue reliability

[0021]

[0022] Among them, k represents the kth step of iteration; after the final reliability index β is obtained after the iteration is completed, the structural failure probability can be calculated

[0023] P f (t) = P(g(t) = a th - a(t) < 0) = Φ(-β)

[0024] The structural failure risk index can be further defined through the failure probability, and the structural failure risk index is used as a parameter to characterize the structural state. The relevant formula is as follows:

[0025]

[0026] Among them, P f [F(t i )|θ] represents the probability of no failure in the previous i - 1 time periods and failure in the i - th time period. h(t i ) is the structural failure risk function, and its value can be used as the structural failure risk index.

[0027] Furthermore, the specific calculation of the prior analysis cost in step one is as follows: According to the cost model and the structural state probability model, based on the theory of maximum expected utility, the most preferred prior decision a opt and the corresponding prior analysis cost C pri are obtained. The prior analysis cost is calculated as shown in the following formula:

[0028]

[0029] Among them, θ is the parameter affecting the structural state probability model, and f θ is the structural state probability model; C T represents the total cost in the early warning decision - making process, which is composed of the structural failure cost C F , the structural maintenance cost C R , and the structural operation cost C O .

[0030] Furthermore, step two is specifically as follows:

[0031] Step 2.1: Predict the distribution of short - term future monitoring data: Based on the current monitoring data, update the relevant parameters of the monitoring data distribution through Bayes' formula, and use the updated data distribution as the short - term future monitoring data distribution;

[0032] Step 2.2: Conduct pre - posterior analysis: Perform multiple samplings from the predicted short - term future monitoring data distribution. For each sample, conduct posterior analysis. The cost model used is the same as that in the prior analysis, and the structural state probability model is updated using Bayes' formula as shown in the following formula:

[0033]

[0034] Among them, f x (x(t)|Θ(t)) is the likelihood function, which can be obtained from the structural state monitoring data;

[0035] Step 2.3. Calculate the posterior analysis cost: For each data sample collected from the predicted monitoring data distribution, based on the expected utility theory, obtain the optimal posterior decision a' opt and the corresponding posterior analysis cost C pos , and the posterior analysis cost is calculated as follows:

[0036] C pos = ∫ Θ C T (a' opt , Θ|x(f Θ|x (Θ|x)dθ.

[0037] Furthermore, the calculation of the information value in Step 3 is specifically as follows: Based on the prior analysis cost obtained in Step 1, the posterior analysis cost obtained in Step 2, and the predicted monitoring data distribution, calculate the information value. The calculation formula of the information value is as follows:

[0038]

[0039] where X represents the set of all possible structural monitoring data samples, that is, the predicted monitoring data distribution.

[0040] Furthermore, the calculation of the optimal warning threshold in Step 3 is specifically as follows: Different warning thresholds h will result in different warning costs C T . In order to obtain the highest warning benefit, take the warning threshold as the variable to be optimized, and obtain the optimal warning threshold h by maximizing the information value * , that is:

[0041] C T = C T (a, θ, h)

[0042]

[0043] where h * represents the optimal warning threshold when the supplementary information sample set is X; in the structural warning application scenario based on Bayesian decision-making, the prior decision cost is a fixed value and is not affected by the structural monitoring data or other supplementary information. Therefore, maximizing the information value is also equivalent to minimizing the expected value of the posterior analysis cost in the post-posterior analysis, that is:

[0044]

[0045] Furthermore, Step 4 is specifically as follows:

[0046] Step 4.1. Make corresponding curves based on the structural reliability, failure probability, and failure risk indicators obtained for each time period under the current monitoring data, and determine the interval where the best warning threshold is located;

[0047] Step 4.2. Determine the warning time: According to the failure risk index curve, when the failure risk index value in a certain time period exceeds the warning threshold, the previous time period is taken as the warning time.

[0048] The present invention also provides an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of the bridge structure risk warning method based on Bayesian decision-making and information value are implemented.

[0049] The present invention also provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps of the bridge structure risk warning method based on Bayesian decision-making and information value are implemented.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0051] Aiming at the problems existing in the traditional bridge warning method, the present invention adopts a method based on Bayesian decision-making and information value to realize structural risk warning. The proposed method comprehensively considers factors such as the degradation of the bridge structure health state and the direct and indirect costs involved in the warning decision, and fully utilizes the structural state monitoring data to update the structural health state in real time to ensure the most cost-effective adaptive warning decision under the comprehensive consideration of structural performance degradation and structural failure risk, and has multiple advantages compared with the traditional single-index over-limit alarm method. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings according to the provided drawings without creative efforts.

[0053] Figure 1 It is a flowchart of the bridge structure risk warning method based on Bayesian decision-making and information value according to the present invention.

[0054] Figure 2 It is a schematic diagram of the bridge finite element model in the embodiment of the present invention.

[0055] Figure 3 It is a stress-time history diagram of the mid-span section in the embodiment of the present invention.

[0056] Figure 4 It is a structural reliability, failure probability, and failure risk index diagram obtained based on the current monitoring data in the embodiment of the present invention.

[0057] Figure 5 It is the stress-time history diagram obtained by sampling the future short-term prediction data distribution in the embodiment of the present invention.

[0058] Figure 6 It is the relationship curve diagram of the decision-making cost and information value and the risk function value in the embodiment of the present invention.

[0059] Figure 7 It is the optimal early warning threshold and the best early warning time diagram in the embodiment of the present invention. Detailed implementation manners

[0060] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0061] In conjunction with Figures 1-7 , the present invention proposes a bridge structure risk early warning method based on Bayesian decision-making and information value. The method includes the following steps:

[0062] Step 1, perform Bayesian prior analysis. According to the Bayesian prior analysis theory, construct a corresponding cost model and a structural state probability model, and define a specific decision space. The cost model includes the structural failure cost, the structural maintenance cost, and the structural operation cost. The structural state probability model is obtained through fatigue reliability analysis based on crack propagation. The decision space depends on the specific application scenario. Based on the maximum expected utility theory, obtain the most prior decision and the corresponding prior analysis cost under the currently available monitoring data.

[0063] Step 2, perform Bayesian pre-posterior analysis. Based on the currently monitored data, predict the future short-term monitored data distribution. For each possibility of the monitored data, perform posterior analysis, and then based on the maximum expected utility theory, obtain the optimal decision and the posterior analysis cost under each possibility of the monitored data. The cost model and decision space used are the same as those in Step 1. The structural state probability model used is obtained by updating the structural state probability model in Step 1 through the monitored data and Bayesian theory.

[0064] Step 3, calculate the information value. According to the future short-term monitored data distribution predicted in Step 2, take the mathematical expectation of the difference between the posterior analysis cost and the prior analysis obtained under each possibility of the monitored data to obtain the information value. Then, by maximizing the information value, obtain the optimal early warning threshold under the Bayesian pre-posterior analysis, which can ensure the maximum expected utility under the future monitored data distribution.

[0065] Step 4: Conduct structural early warning. Based on the structural reliability index, failure probability, failure risk function obtained through fatigue reliability analysis, and the optimal early warning threshold obtained through information value analysis, conduct early warning judgment. When the failure risk function value in a certain time period is higher than the optimal early warning threshold, give an early warning in the previous time period.

[0066] The specific content of Step 1 is as follows:

[0067] Step 1.1: Construct a cost model. The cost model mainly includes the structural failure cost C F , the structural maintenance cost C R , and the structural operation cost C O . The failure cost includes the direct cost related to the direct damage of the structure and the indirect cost caused by the loss of structural function, etc. The maintenance cost includes the human and material costs required for maintenance and the indirect cost caused by the structural maintenance, etc. The structural operation cost includes the economic loss cost caused by control measures, etc. The calculation methods of the failure cost C F and the maintenance cost C R are shown in the following formula:

[0068]

[0069] Where represents the economic loss caused by the structural failure, is the cost required for a single structural maintenance, r is the discount rate, and t w represents the early warning time. The calculation of the operation cost C O can be determined according to the specific structure and scenario.

[0070] Step 1.2: Model the structural state probability. Based on the fatigue crack growth theory, conduct structural fatigue reliability analysis to obtain the structural reliability index and failure probability within a certain future time. The relevant formulas of the fatigue crack growth theory are as follows.

[0071]

[0072] Among them, a represents the fatigue crack depth; n represents the number of cycles of the fatigue load; a(n) represents the fatigue crack depth at the nth cycle of the fatigue load; C m and m are both fatigue crack growth constants, which can be determined through material tests; G is the crack geometry correction coefficient, usually a function of the fatigue crack depth; Δσ is the equivalent fatigue stress amplitude. For the convenience of fatigue reliability analysis, it can be assumed that the value of the geometry correction coefficient is a constant 1, and the following formula can be obtained by integration:

[0073]

[0074] Among them, \(a_0\) represents the initial fatigue crack depth; \(v\) represents the mean value of the number of load cycles, which can be determined according to a preset time interval; \(a(t)\) represents the fatigue crack depth at time \(t\). The fatigue limit state equation can be defined as:

[0075] \(g(t)=a\) th \(-a(t)\)

[0076] Among them, \(a\) th is the limit threshold of the fatigue crack. The HL-RF algorithm is used to solve the fatigue reliability:

[0077]

[0078] Among them, \(k\) represents the \(k\)-th step of iteration. After the final reliability index \(\beta\) is obtained after the iteration is completed, the structural failure probability can be calculated:

[0079] \(P\) f (t)=P(g(t)=a th \(-a(t)\lt0)=\varPhi(-\beta)\)

[0080] Through the failure probability, the structural failure risk index can be further defined, so as to use the structural failure risk index as a parameter to characterize the structural state. The relevant formulas are as follows:

[0081]

[0082] Among them, \(P\) f [F(t i )|\theta] represents the probability that the structure has not failed in the previous \(i - 1\) time periods and fails in the \(i\)-th time period. \(h(t\) i ) is the structural failure risk function, and its value can be used as the structural failure risk index. This index is related to various factors such as the structural material parameters and the structural stress state.

[0083] Step 1.3. Calculate the prior analysis cost. First, determine the decision space, which should be determined according to the specific application scenario. Then, based on the cost model and the structural state probability model obtained in Steps 1.1 and 1.2, and based on the theory of maximum expected utility, the most prior decision \(a\) opt and the corresponding prior analysis cost \(C\) pri can be obtained. The prior cost is calculated as shown in the following formula:

[0084]

[0085] Among them, \(\theta\) is the parameter affecting the structural state probability model, and \(f\) θ is the structural state probability model; \(C\) T represents the total cost in the early warning decision-making process, which is composed of the structural failure cost \(C\) F , the structural maintenance cost \(C\) Rand the structural operation cost C O Composed of

[0086] The specific content of Step 2 is as follows:

[0087] Step 2.1: Predict the distribution of short-term future monitoring data. Based on the current monitoring data, update the relevant parameters of the monitoring data distribution through the Bayesian formula, and use the updated data distribution as the short-term future monitoring data distribution.

[0088] Step 2.2: Conduct pre-posterior analysis. Conduct multiple samplings from the predicted future short-term monitoring data distribution. For each sample, conduct posterior analysis. The cost model and decision space used are the same as those in the prior analysis. The structural state probability model is updated using the Bayesian formula as shown below:

[0089]

[0090] where f x (x(t)|Θ(t)) is the likelihood function, which can be obtained from the structural state monitoring data.

[0091] Step 2.3: Calculate the posterior analysis cost. For each data sample collected from the predicted monitoring data distribution, based on the expected utility theory, the optimal posterior decision a' opt and the corresponding posterior analysis cost C pos can be obtained. The calculation formula for the posterior analysis cost is as shown below:

[0092]

[0093] The specific content of Step 3 is as follows:

[0094] Step 3.1: Calculate the value of information. Based on the prior analysis cost obtained in Step 1, the posterior analysis cost obtained in Step 2, and the predicted monitoring data distribution, calculate the value of information. The calculation formula for the value of information is as shown below:

[0095]

[0096] where X represents the set of all possible structural monitoring data samples, that is, the predicted monitoring data distribution.

[0097] Step 3.2: Calculate the optimal warning threshold. Different warning thresholds h will result in different warning costs C T . In order to obtain the highest warning benefit, take the warning threshold as the variable to be optimized, and obtain the optimal warning threshold h * by maximizing the value of information, that is:

[0098] C T = C T(a, θ, h)

[0099]

[0100] Among them, h * represents the optimal warning threshold when the supplementary information sample set is X. In the structural warning application scenario based on Bayesian decision-making, the prior decision cost is a fixed value and is not affected by the structural monitoring data or other supplementary information. Therefore, maximizing the information value is also equivalent to minimizing the expected value of the posterior cost in the prognostic analysis, that is:

[0101]

[0102] Step four is specifically as follows:

[0103] Step 4.1: Make corresponding curves based on the structural reliability, failure probability, and failure risk indicators obtained in each time period under the current monitoring data, and determine the interval where the best warning threshold is located.

[0104] Step 4.2: Determine the warning time. According to the failure risk indicator curve, when the failure risk indicator value in a certain time period exceeds the warning threshold, the previous time period is used as the warning time.

[0105] Embodiment

[0106] This embodiment applies the present invention to the finite element simulation data set of a certain bridge in Nanjing. The flowchart of the method of the present invention is as Figure 1 shown, and the finite element model established in this embodiment is as Figure 2 shown. In this embodiment, by simulating random vehicle flows on the bridge, a stress-time history diagram at the mid-span of the main span is obtained, as Figure 3 shown.

[0107] Specifically, in this embodiment, each warning cost is set as a multiple of the constant c0, and the economic loss caused by the structural failure takes a value of 1×10 4 c0, the cost required for a single structural repair takes a value of 1×10 2 c0, the operation cost takes a value of 2×10 1 c0, and the discount rate r takes a value of 0.02. The parameter settings for the structural fatigue reliability analysis include: a0 is an exponential distribution with a mean of 0.1 and a standard deviation of 0.01, a th is a normal distribution with a mean of 50 and a standard deviation of 10, Δσ is a normal distribution with a mean of 17 and a standard deviation of 3.2, m is a normal distribution with a mean of 3 and a standard deviation of 0.1, C m is a lognormal distribution with a mean of 2.25×10 -14 and a standard deviation of 1.75×10 -15 , and v takes a value of 3×106 。The structural reliability, failure probability, and failure risk index curves obtained from fatigue reliability analysis are as follows Figure 4 shown. The decision space in the prior analysis includes two decisions: not taking early warning and post - measure for the bridge, and taking early warning for the bridge and closing and repairing the bridge. Based on the theory of maximizing expected utility, the optimal decision cost in the prior analysis scenario is 97.433c0.

[0108] Specifically, step two is as follows: Based on the existing stress - time history diagram, predict the short - term future stress - time distribution based on Bayes' formula. Then, perform Bayesian pre - posterior analysis by sampling from this distribution. The stress - time history diagrams obtained from some of the sampled samples are as follows Figure 5 shown.

[0109] Specifically, step three is as follows: Calculate the value of information by using the prior analysis cost obtained in step one and the multiple posterior analysis costs calculated after sampling in step two. Take the early warning threshold as the variable to be optimized, and aim to maximize the value of information. Calculate the optimal early warning threshold so that it has the maximum early warning expected utility in the future short - term prediction data distribution. The calculated result is h * = 2.375×10 -7 , and the curves of the decision cost, value of information, and the risk function value are as follows Figure 6 shown.

[0110] Specifically, step four is as follows: Determine the early warning time through the optimal early warning threshold obtained in step three. According to the failure risk index curve, when the failure risk index value in a certain time period exceeds the early warning threshold, take the previous time period as the early warning time. As follows Figure 7 shown, the best early warning time is in the 27th time period.

[0111] The present invention also proposes an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of the bridge structure risk early warning method based on Bayesian decision - making and information value are implemented.

[0112] The present invention also proposes a computer - readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps of the bridge structure risk early warning method based on Bayesian decision - making and information value are implemented.

[0113] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read only memory (ROM), a programmable ROM (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and direct rambus RAM (DRRAM). It should be noted that the memory of the method described in the present invention is intended to include but not limited to these and any other suitable types of memory.

[0114] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from a website, computer, server, or data center to another website, computer, server, or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wirelessly (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. that includes one or more available media integrated. The available medium can be a magnetic medium (such as a floppy disk, hard disk, magnetic tape), an optical medium (such as a high-density digital video disc (DVD)), or a semiconductor medium (such as a solid state disc (SSD)), etc.

[0115] In the implementation process, the steps of the above method can be completed by the integrated logic circuit of the hardware in the processor or the instructions in the form of software. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as being executed by the hardware processor or executed by the combination of the hardware and software modules in the processor. The software module can be located in a mature storage medium in the art such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here.

[0116] It should be noted that the processor in the embodiments of the present application may be an integrated circuit chip with signal processing capabilities. In the implementation process, the steps of the above method embodiments can be completed by the integrated logic circuit in the hardware of the processor or instructions in software form. The above-mentioned processor may be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present application. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as being executed and completed by the hardware decoding processor, or executed and completed by a combination of the hardware and software modules in the decoding processor. The software module may be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method.

[0117] The above has introduced in detail a bridge structure risk early warning method based on Bayesian decision-making and information value proposed by the present invention. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A bridge structure risk early warning method based on Bayesian decision-making and information value, characterized in that The method includes the following steps: Step 1, perform Bayesian prior analysis: According to the Bayesian prior analysis theory, construct corresponding cost models and structural state probability models; the cost models include structural failure costs, structural maintenance costs, and structural operation costs, and the structural state probability models are obtained through fatigue reliability analysis based on crack propagation, and then based on the theory of maximum expected utility, the most preferred prior decision and the corresponding prior analysis cost under the currently available monitoring data are obtained; Step 2, perform Bayesian pre-posterior analysis: Based on the current monitoring data, predict the distribution of future short-term monitoring data. For each possibility of the monitoring data, perform posterior analysis, and then based on the theory of maximum expected utility, obtain the optimal decision and posterior analysis cost for each possibility of the monitoring data; the cost model used is the same as the cost model in Step 1, and the structural state probability model used is obtained by updating the structural state probability model in Step 1 through the monitoring data and Bayesian theory; Step 3, calculate the value of information: According to the distribution of future short-term monitoring data predicted in Step 2, calculate the mathematical expectation of the difference between the posterior analysis cost and the prior analysis for each possibility of the monitoring data to obtain the value of information; then, by maximizing the value of information, obtain the optimal warning threshold under the Bayesian pre-posterior analysis, and this threshold can ensure the maximum expected utility under the future monitoring data distribution; Step 4, perform bridge structure warning: According to the structural reliability index, failure probability, and failure risk function obtained through fatigue reliability analysis, as well as the optimal warning threshold obtained through the value of information analysis, perform warning judgment. When the failure risk function value in a certain time period is higher than the optimal warning threshold, give a warning in the previous time period.

2. The method according to claim 1, characterized in that, The specific construction of the cost model in Step 1 is as follows: The cost model includes the structural failure cost C F , the structural maintenance cost C R , and the structural operation cost C O ; the structural failure cost includes the direct cost related to the structural damage and the indirect cost caused by the loss of the structural function; the structural maintenance cost includes the human and material costs required for maintenance and the indirect cost caused by the structural maintenance; the structural operation cost includes the economic loss cost caused by the control measures; the calculation methods of the structural failure cost C F and the structural maintenance cost C R are shown as follows: wherein represents the economic loss caused by structural failure, is the cost required for a single repair of the structure, r is the discount rate, and t w represents the warning time; the calculation of the operating cost C O can be determined according to the specific structure and scenario.

3. The method according to claim 2, wherein In Step 1, the modeling of the structural state probability model is specifically as follows: Based on the fatigue crack propagation theory, perform structural fatigue reliability analysis to obtain the structural reliability index and failure probability within a certain future time; the relevant formulas of the fatigue crack propagation theory are as follows: where a represents the fatigue crack depth; n represents the number of cycles of the fatigue load; a(n) represents the fatigue crack depth at n cycles of the fatigue load; C m and m are both fatigue crack growth constants, which can be determined through material tests; G is the crack geometry correction factor; Δσ is the equivalent fatigue stress amplitude; for the convenience of fatigue reliability analysis, it is assumed that the value of the geometry correction factor is a constant 1, and thus the following formula can be obtained by integration: Among them, a0 represents the initial fatigue crack depth; v represents the mean value of the number of load cycles, which can be determined according to a preset time interval; a(t) represents the fatigue crack depth at time t; the fatigue limit state equation can be defined as: g(t) = a th -a(t) Among them, a th is the limit threshold of the fatigue crack; the HL-RF algorithm is used to solve the fatigue reliability: Among them, k represents the kth step of iteration; after the iteration is completed to obtain the final reliability index β, the structural failure probability can be calculated: P f P(t) = P(g(t)=a th -a(t)<0) = Φ(-β) Through the failure probability, the structural failure risk index can be further defined, so as to use the structural failure risk index as a parameter representing the structural state. The relevant formulas are as follows: Among them, P f [F(t i )|θ] represents the probability that it has not failed in the previous i - 1 time periods and fails in the i-th time period, and h(t i ) is the structural failure risk function, and its value can be used as a structural failure risk indicator.

4. The method according to claim 3, wherein The specific calculation of the prior analysis cost in Step 1 is as follows: According to the cost model and the structural state probability model, based on the theory of maximum expected utility, the most preferred prior decision a opt and the corresponding prior analysis cost C pri are obtained. The prior analysis cost is calculated as shown in the following formula: where θ is a parameter affecting the structural state probability model, and f θ is the structural state probability model; C T represents the total cost in the early warning decision-making process, which consists of the structural failure cost C F , the structural maintenance cost C R , and the structural operation cost C O .

5. The method according to claim 1, characterized in that, The specific content of Step 2 is as follows: Step 2.1, predict the distribution of short-term future monitoring data: Based on the current monitoring data, update the relevant parameters of the monitoring data distribution through the Bayesian formula, and use the updated data distribution as the distribution of short-term future monitoring data; Step 2.2, perform pre-posterior analysis: Take multiple samples from the predicted distribution of future short-term monitoring data. For each sample, perform posterior analysis. The cost model used is the same as the cost model in the prior analysis, and the structural state probability model is updated by the Bayesian formula, as shown in the following formula: where f x (x(t)|Θ(t)) is the likelihood function, which can be obtained from the structural state monitoring data; Step 2.3, Calculate the posterior analysis cost: For each data sample collected from the predicted monitoring data distribution, based on the expected utility theory, obtain the optimal posterior decision a' opt and the corresponding posterior analysis cost C pos , and the posterior analysis cost is calculated as shown in the following formula: C pos = ∫ Θ C T (a' opt , Θ|x) f Θ|x (Θ|x) dθ。 6. The method according to claim 1, characterized in that The calculation of the information value in step three is specifically as follows: Based on the prior analysis cost obtained in step one, the posterior analysis cost obtained in step two, and the predicted distribution of monitoring data, calculate the information value. The calculation formula of the information value is as follows: Where X represents the set of all possible structural monitoring data samples, that is, the predicted distribution of monitoring data.

7. The method according to claim 6, wherein In step three, the specific calculation of the optimal warning threshold is as follows: different warning thresholds h will result in different warning costs C T , in order to obtain the highest warning benefit, the warning threshold is taken as the variable to be optimized, and the optimal warning threshold h is obtained by maximizing the information value * , that is: C T = C T (a, θ, h) where h * represents the optimal warning threshold when the supplementary information sample set is X; in the structural warning application scenario based on Bayesian decision-making, the prior decision cost is a fixed value and is not affected by structural monitoring data or other supplementary information. Therefore, maximizing the information value is also equivalent to minimizing the expected value of the posterior analysis cost in the pre-posterior analysis, that is:

8. The method according to claim 1, characterized in that The specific content of step four is as follows: Step 4.1: Make corresponding curves based on the structural reliability, failure probability, and failure risk index obtained in each time period under the current monitoring data, and determine the interval where the optimal warning threshold is located; Step 4.2: Determine the warning time: According to the failure risk index curve, when the failure risk index value in a certain time period exceeds the warning threshold, the previous time period is used as the warning time.

9. An electronic device, comprising a memory and a processor, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-8.

10. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, it implements the steps of the method according to any one of claims 1-8.

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