A bridge structure risk early warning method based on bayesian decision and information value

Abstract

The application provides a bridge structure risk early warning method based on Bayesian decision and information value. The method firstly carries out Bayesian prior analysis through structure monitoring data, a cost model includes structure failure cost, maintenance cost and control cost, and a structure state model is obtained through structure fatigue reliability analysis. Next, Bayesian post-analysis is carried out, the distribution of short-term future monitoring data is predicted based on current monitoring data, then the possibility of each kind of monitoring data is analyzed, structure fatigue reliability analysis is carried out and the corresponding failure risk index is calculated, and then the information value is calculated based on the cost model. Finally, the optimal structure early warning threshold under the Bayesian post-analysis is obtained by maximizing the information value, so that the best early warning time is determined. The method provides an adaptive structure risk early warning method which comprehensively considers early warning cost and structure performance degradation, and can realize fast early warning decision with safety guarantee and economic benefit.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of civil engineering, and particularly relates to a bridge structure risk early warning method based on Bayesian decision and information value. BACKGROUND

[0002] Bridges are an indispensable part of the transportation network, ensuring smooth communication between regions and the continuity of economic activities. During their service life, the structural performance of bridges gradually deteriorates. Early warning systems can detect potential risks in the structure in advance, issue timely warnings, and prevent potential accidents, ensuring the safety of people's lives and property. At the same time, such systems can help relevant departments develop more scientific maintenance and repair plans by continuously monitoring the health of bridges, avoiding long-term traffic disruptions due to sudden failures, and improving 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.

[0003] Traditional methods usually use single-index overrun alarms, which only make corresponding early warning decisions when the monitored indicators exceed the pre-set early warning threshold. This single threshold setting does not fully consider the actual situation of the bridge under different working conditions, as the bridge is subjected to the coupling effects of strong winds, temperature changes, vehicle loads, and other environmental factors. Single-index overrun alarms may not accurately reflect the true safety state of the bridge. At the same time, existing bridge early warning methods are mostly static, i.e., they often use constant early warning thresholds set at the initial stage of bridge construction based on design parameters, without considering changes in structural effects or structural performance degradation due to various environmental effects and making corrections. This may result in the early warning system failing to issue warnings in a timely manner when the bridge has already experienced significant safety risks (false negatives) or triggering alarms due to temporary sensor failures or data transmission interference (false positives). On the other hand, existing early warning methods do not systematically consider the cost of early warning behavior, and relying solely on single-index overrun alarms may result in frequent false positives and false negatives, causing a waste of manpower, resources, and economic losses. Therefore, systematically considering the cost-effectiveness of bridge early warning is beneficial to the long-term support and sustainable development of bridge structure early warning systems, ensuring the long-term safe operation of bridges. SUMMARY

[0004] The application aims to solve the problems in the prior art and provides a bridge structure risk early warning method based on Bayesian decision and information value. The method is suitable for early warning of potential risks to the structure based on monitoring data.

[0005] The application is realized by the following technical scheme, the application provides a bridge structure risk early warning method based on Bayesian decision and information value, the method comprises the following steps:

[0006] Step one, Bayesian prior analysis is carried out: according to the Bayesian prior analysis theory, a corresponding cost model and a structure state probability model are constructed; the cost model comprises structure failure cost, structure maintenance cost and structure operation cost, the structure state probability model is obtained through fatigue reliability analysis based on crack propagation, and then the optimal prior decision under the current monitoring data and the corresponding prior analysis cost are obtained based on the expected utility maximization theory;

[0007] Step two, Bayesian post-prior analysis is carried out: based on the future short-term monitoring data distribution predicted by the current monitoring data, post-prior analysis is carried out for each monitoring data possibility, and then the optimal decision under each monitoring data possibility and the post-prior analysis cost are obtained based on the expected utility maximization theory; wherein the cost model used is the same as the cost model in step one, and the structure state probability model used is obtained by updating the structure state probability model in step one through monitoring data and Bayesian theory;

[0008] Step three, information value is calculated: the difference between the post-prior analysis cost and the prior analysis cost under each monitoring data possibility is mathematically expected according to the future short-term monitoring data distribution predicted in step two, and the information value is obtained; then the optimal early warning threshold under the Bayesian post-prior analysis is obtained by maximizing the information value, which can ensure the maximum expected utility under the future monitoring data distribution;

[0009] Step four, bridge structure early warning is carried out: according to the structure reliability index, failure probability and failure risk function obtained through fatigue reliability analysis, and the optimal early warning threshold obtained through information value analysis, early warning judgment is carried out, and when the failure risk function value of a time period is higher than the optimal early warning threshold, early warning is carried out in the last time period.

[0010] Further, the cost model is constructed in step one, specifically: the cost model comprises structure failure cost C F , structure maintenance cost C R and structure operation cost C O ; the structure failure cost comprises direct cost related to structure damage and indirect cost caused by structure function loss; the structure maintenance cost comprises manpower and material resources cost required for maintenance and indirect cost caused by structure maintenance; the structure operation cost comprises economic loss cost caused by control measures; the calculation methods of the structure failure cost C F and the structure maintenance cost C R are as follows:

[0011]

[0012] 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, t w represents the time of the early warning; the operating cost C O The calculation can be determined according to the specific structure and scenario.

[0013] Further, the structural state probability model in step one is specifically: based on the fatigue crack propagation theory, the fatigue reliability of the structure is analyzed, and the structural reliability index and failure probability in a certain time in the future are obtained; the related formula of the fatigue crack propagation theory is as follows:

[0014]

[0015]

[0016] wherein a represents the fatigue crack depth; n represents the number of fatigue load cycles; a(n) represents the fatigue crack depth at the fatigue load cycle n; C m and m are both fatigue crack propagation constants, which can be determined by material test; G is a crack geometry correction coefficient; Δσ is an equivalent fatigue stress amplitude; in order to facilitate fatigue reliability analysis, it is assumed that the value of the geometry correction coefficient is constant 1, so that the following formula can be integrated:

[0017]

[0018] wherein a0 represents the initial fatigue crack depth; v represents the mean value of the load cycle number, 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] wherein a th is the limit threshold value of the fatigue crack; the HL-RF algorithm is used to realize the solution of the fatigue reliability:

[0021]

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

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

[0024] The failure probability can be used to further define a structural failure risk index, which can then be 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 that the device has not failed in the first i-1 time periods and fails in the i-th time period, h(t) i ) is a structural failure risk function, and its value can be used as a structural failure risk index.

[0027] Furthermore, the calculation of the prior analysis cost in step one specifically involves: based on the cost model and the structural state probability model, and using the expected utility maximization theory, obtaining the highest priority prior decision a. opt And the corresponding prior analysis cost C pri The prior analysis cost calculation is shown in the following formula:

[0028]

[0029] Where θ is a parameter affecting the probabilistic model of structural state, f θ For structural state probabilistic models; C T The total cost in the early warning decision-making process is represented by the structural failure cost C. F Structural maintenance cost C R and structural operating costs C O composition.

[0030] Furthermore, step two specifically involves:

[0031] Step 2.1 Predicting the distribution of monitoring data in the short term: Based on the current monitoring data, update the relevant parameters of the monitoring data distribution using the Bayesian formula, and use the updated data distribution as the distribution of monitoring data in the short term;

[0032] Step 2.2: Perform posterior analysis: Multiple samples are taken from the predicted distribution of short-term monitoring data. For each sample, a posterior analysis is performed. The cost model used is consistent with the cost model used in the prior analysis. The structural state probability model is updated using Bayes' theorem, as shown in the following equation:

[0033]

[0034] Among them, f x (x(t)|Θ(t)) is the likelihood function, which can be obtained from 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 expected utility theory, obtain the optimal posterior decision a'. opt And the corresponding posterior analysis cost C pos The posterior analysis cost calculation is shown in the following formula:

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

[0037] Furthermore, the calculation of information value in step three specifically involves: 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, the information value is calculated. The formula for calculating information value is shown below:

[0038]

[0039] Where X represents the set of all possible structural monitoring data samples, i.e., the predicted distribution of monitoring data.

[0040] Furthermore, the calculation of the optimal warning threshold in step three specifically involves: different warning thresholds h will lead to different warning costs C. T To obtain the highest early warning benefit, the early warning threshold is treated as a variable to be optimized, and the optimal early warning threshold h is obtained by maximizing the information value. * ,Right now:

[0041] C T =C T (a,θ,h)

[0042]

[0043] Among them, h * This represents the optimal warning threshold when the supplementary information sample set is X. In structural early warning applications based on Bayesian decision-making, the prior decision cost is a fixed value unaffected by structural monitoring data or other supplementary information. Therefore, maximizing the information value is equivalent to minimizing the expected value of the posterior analysis cost during pre- and posterior analysis, i.e.:

[0044]

[0045] Furthermore, step four specifically involves:

[0046] Step 4.1: Based on the structural reliability, failure probability, and failure risk indicators obtained from the current monitoring data for each time period, create corresponding curves and determine the range of the optimal early warning threshold.

[0047] Step 4.2, determining the early warning time: according to the failure risk index curve, when the failure risk index value of a certain time period exceeds the early warning threshold, the last time period is taken as the early warning time.

[0048] The application further provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the bridge structure risk early warning method based on Bayesian decision and information value when executing the computer program.

[0049] The application further provides a computer readable storage medium for storing computer instructions, wherein the computer instructions implement the steps of the bridge structure risk early warning method based on Bayesian decision and information value when executed by a processor.

[0050] Compared with the prior art, the application has the following beneficial effects:

[0051] The application aims at the problems in the traditional bridge early warning method, and realizes structure risk early warning by using the method based on Bayesian decision and information value. The proposed method comprehensively considers the bridge structure health state degradation and direct and indirect costs involved in the early warning decision, and fully utilizes the structure state monitoring data to update the structure health state in real time, so as to realize the most economic self-adaptive early warning decision under the condition of comprehensively considering the structure performance degradation and structure failure risk, and has many advantages compared with the traditional single index overrun alarm method. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only constitute the embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of the provided drawings.

[0053] Figure 1 The application further provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the bridge structure risk early warning method based on Bayesian decision and information value when executing the computer program.

[0054] Figure 2 The application further provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the bridge structure risk early warning method based on Bayesian decision and information value when executing the computer program.

[0055] Figure 3 The application further provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the bridge structure risk early warning method based on Bayesian decision and information value when executing the computer program.

[0056] Figure 4 The application further provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the bridge structure risk early warning method based on Bayesian decision and information value when executing the computer program.

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

[0058] Figure 6 A relationship curve between the decision cost, the information value and the risk function value in the embodiment of the present application.

[0059] Figure 7 A diagram of the optimal early warning threshold and the best early warning time in the embodiment of the present application. DETAILED DESCRIPTION

[0060] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the scope of protection of the present application.

[0061] In combination with Figures 1-7 The present application proposes a bridge structure risk early warning method based on Bayesian decision and information value, which comprises the following steps:

[0062] Step one, Bayesian prior analysis. According to the Bayesian prior analysis theory, a corresponding cost model and a structure state probability model are constructed, and a specific decision space is defined. The cost model includes structure failure cost, structure maintenance cost and structure operation cost, the structure state probability model is obtained through fatigue reliability analysis based on crack propagation, and the decision space depends on the specific application scenario. Based on the expected utility maximization theory, the optimal prior decision under the current monitoring data and the corresponding prior analysis cost are obtained.

[0063] Step two, Bayesian post-prior analysis. Based on the prediction of the future short-term monitoring data distribution, the post-prior analysis is performed for each possibility of monitoring data, and the optimal decision and the post-prior analysis cost under each possibility of monitoring data are obtained based on the expected utility maximization theory. The cost model and the decision space used are the same as those in step one, and the structure state probability model used is obtained by updating the structure state probability model in step one through monitoring data and Bayesian theory.

[0064] Step three, information value calculation. According to the future short-term monitoring data distribution predicted in step two, the mathematical expectation of the difference between the post-prior analysis cost and the prior analysis cost under each possibility of monitoring data is obtained, and the information value is obtained. Then, by maximizing the information value, the optimal early warning threshold under the Bayesian post-prior analysis is obtained, which can guarantee the maximum expected utility under the future monitoring data distribution.

[0065] Step four, structure early warning. According to the structure reliability index, failure probability and failure risk function obtained by fatigue reliability analysis, and the optimal early warning threshold obtained by information value analysis, early warning is judged, and early warning is given in the last time period when the failure risk function value of a certain time period is higher than the optimal early warning threshold.

[0066] The step one is specifically:

[0067] Step 1.1, constructing cost model. The cost model mainly includes structure failure cost C F , structure maintenance cost C R and structure operation cost C O . Failure cost includes direct cost related to direct damage of structure and indirect cost caused by loss of structure function, maintenance cost includes manpower and material cost required for maintenance and indirect cost caused by structure maintenance, and structure operation cost includes economic loss cost caused by control measures. The calculation methods of failure cost C F and maintenance cost C R are as follows:

[0068]

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

[0070] Step 1.2, structure state probability modeling. Based on fatigue crack propagation theory, structure fatigue reliability analysis is carried out to obtain structure reliability index and failure probability in future certain time. The related formula of fatigue crack propagation theory is as follows.

[0071]

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

[0073]

[0074] where a0 represents the initial fatigue crack depth; v represents the mean value of the load cycle number, which can be determined according to a preset time interval; and 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] where a th is the limit threshold value of the fatigue crack. The HL-RF algorithm is adopted to solve the fatigue reliability:

[0077]

[0078] where k represents the kth iteration step. After the final reliability index β is obtained through iteration, the structure failure probability can be calculated as:

[0079] P f (t) = P(g(t) = a th -a(t) < 0) = Φ(-β)

[0080] The structure failure risk index can be further defined by the failure probability, so as to take the structure failure risk index as a parameter representing the structure state, and the related formula is as follows:

[0081]

[0082] where P f [F(t i )|θ] represents the probability that the structure does not fail in the first i-1 time periods and fails in the i time period, and h(t i ) is the structure failure risk function, the value of which can be taken as the structure failure risk index, which is related to the structure material parameters and the structure stress state and the like.

[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 structure state probability model obtained in steps 1.1 and 1.2, the optimal prior decision a opt and the corresponding prior analysis cost C pri can be obtained based on the expected utility maximization theory, and the prior cost is calculated as follows:

[0084]

[0085] where θ is a parameter affecting the structure state probability model, f θ is the structure state probability model; and C T represents the total cost in the early warning decision process, which is composed of the structure failure cost C F , the structure maintenance cost C Rand the structural operation cost C O compositions.

[0086] The step two is specifically as follows:

[0087] Step 2.1, predicting short-term future monitoring data distribution. Based on the current monitoring data, the related parameters of the monitoring data distribution are updated through the Bayesian formula, and the updated data distribution is taken as the short-term future monitoring data distribution.

[0088] Step 2.2, performing post-prior analysis. A plurality of samples are sampled from the predicted short-term future monitoring data distribution, and for each sample, post-prior analysis is performed, the cost model and the decision space used are consistent with the cost model and the decision space in the prior analysis, and the structural state probability model is updated through the Bayesian formula, as shown in the following formula:

[0089]

[0090] Wherein, f x (x(t)|Θ(t)) is a likelihood function, which can be obtained through structural state monitoring data.

[0091] Step 2.3, calculating post-prior analysis cost. For each data sample collected from the predicted monitoring data distribution, based on the expected utility theory, the optimal post-prior decision a' opt and the corresponding post-prior analysis cost C pos are obtained, and the post-prior analysis cost is calculated as shown in the following formula:

[0092]

[0093] The step three is specifically as follows:

[0094] Step 3.1, calculating information value. Based on the prior analysis cost obtained in step one, the post-prior analysis cost obtained in step two and the predicted monitoring data distribution, the information value is calculated, and the calculation formula of the information value is as shown in the following formula:

[0095]

[0096] Wherein, X represents a set of all possible structural monitoring data samples, i.e. the predicted monitoring data distribution.

[0097] Step 3.2, calculating optimal warning threshold. 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 a to-be-optimized variable, and the optimal warning threshold h * is obtained by maximizing the information value, i.e.:

[0098] C T =C T(a, θ, h)

[0099]

[0100] where h * represents the optimal early warning threshold value when the supplementary information sample set is X. In the structural early warning application scenario based on Bayesian decision, the prior decision cost is a fixed value and is not affected by the structural monitoring data or other supplementary information, so maximizing the information value is equivalent to minimizing the expected value of the posteriori cost in the post-analytical stage, i.e.

[0101]

[0102] Step four is specifically:

[0103] Step 4.1, according to the structural reliability, failure probability and failure risk index of each time period obtained under the current monitoring data, the corresponding curve is made, and the interval where the optimal early warning threshold value is located is determined.

[0104] Step 4.2, determine the early warning time. According to the failure risk index curve, when the failure risk index value of a certain time period exceeds the early warning threshold value, the last time period is taken as the early warning time.

[0105] Embodiment

[0106] The present application is applied to the finite element simulation data set of a certain bridge in Nanjing in the present embodiment, the flow chart of the method of the present application is shown in Figure 1 , and the finite element model established in the present embodiment is shown in Figure 2 . In the present embodiment, the stress-time history diagram of the main span central position is obtained by simulating random traffic flow on the bridge, as shown in Figure 3 .

[0107] The step one is specifically: in the present embodiment, each early warning cost is set as a multiple of a constant c0, the economic loss caused by the structural failure is valued at 1×10 4 c0, the cost required for a single maintenance of the structure is valued at 1×10 2 c0, the operation cost is valued at 2×10 1 c0, and the discount rate r is valued at 0.02. The parameter setting when performing structural fatigue reliability analysis includes: 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 is valued at 3×106 The structural reliability, failure probability and failure risk index curves obtained by the fatigue reliability analysis are as shown in Figure 4 The decision space in the prior analysis contains two decisions: no pre-warning and pre-warning measures for the bridge, pre-warning and closing the bridge and repairing the bridge. Based on the expected utility maximization theory, the optimal decision cost under the prior analysis scenario is 97.433c0.

[0108] The step two is specifically: based on the current existing stress-time diagram, the short-term future stress-time distribution is predicted based on the Bayes formula. As shown in Figure 5 .

[0109] The step three is specifically: through the prior analysis cost obtained in the step one and the multiple posterior analysis costs calculated after sampling in the step two, the information value is calculated, the pre-warning threshold is taken as the to-be-optimized variable, and the optimal pre-warning threshold is calculated to maximize the information value, so that the pre-warning expected utility in the future short-term prediction data distribution is the largest. The calculated result is h * = 2.375x10 -7 The curves of the decision cost and the information value and the risk function value are as shown in Figure 6 .

[0110] The step four is specifically: through the optimal pre-warning threshold obtained in the step three, the pre-warning time is determined, and according to the failure risk index curve, when the failure risk index value of a time period exceeds the pre-warning threshold, the previous time period is taken as the pre-warning time. As shown in Figure 7 , the best pre-warning time is located in the 27th time period.

[0111] The application further provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the bridge structure risk pre-warning method based on the Bayes decision and information value when executing the computer program.

[0112] The application further provides a computer readable storage medium for storing computer instructions, wherein the computer instructions implement the steps of the bridge structure risk pre-warning method based on the Bayes decision and information value when executed by a processor.

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

[0114] In the above embodiments, all or part of the methods can be implemented by software, hardware, firmware, or any combination thereof. When implemented by software, all or part of the methods can be implemented 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, all or part of the processes or functions described in the embodiments of the present application are generated. 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 transferred from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center through wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) manner. 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 sets. The available media can be magnetic media (such as floppy disk, hard disk, magnetic tape), optical media (such as high-density digital video disc (DVD)), or semiconductor media (such as solid state disc (SSD)), etc.

[0115] In the implementation process, each step of the above method can be completed by integrated logic circuit of hardware in the processor or instruction in the form of software. The steps of the method disclosed in the embodiments of the present application can be directly embodied as hardware processor execution, or executed by combination of hardware and software modules in the processor. The software module can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, register, and other mature storage media in the art. The storage medium is located in the memory, and the processor reads the information in the memory and combines the 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 can be an integrated circuit chip with processing capability of signals. In the implementation process, each step of the method embodiments can be completed by integrated logic circuits or instructions in the form of software in the processor. The processor mentioned above can be a general processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The disclosed methods, steps and logic block diagrams in the embodiments of the present application can be implemented or executed. The general processor can be a microprocessor or the processor can be any conventional processor. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as hardware code processing executed by the processor, or executed by a combination of hardware and software modules in the code processing processor. The software module can be located in a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, and other mature storage media in the art. The storage medium is located in the memory, and the processor reads the information in the memory and combines the hardware to complete the steps of the above method.

[0117] The above describes in detail the bridge structure risk early warning method based on Bayesian decision and information value. The principle and implementation mode of the present application are described by using specific examples. The above embodiment is only used to help understand the method of the present application and its core idea. Meanwhile, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed. In summary, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A bridge structure risk early warning method based on Bayesian decision and information value, characterized in that, The method comprises the following steps: Step one, Bayesian prior analysis: according to the Bayesian prior analysis theory, the corresponding cost model and structural state probability model are constructed; the cost model includes structural failure cost, structural maintenance cost and structural operation cost, the structural state probability model is obtained through fatigue reliability analysis based on crack propagation, and the optimal prior decision and the corresponding prior analysis cost under the current monitoring data are obtained based on the expected utility maximization theory; Step two, Bayesian posteriori analysis: based on the prediction of future short-term monitoring data distribution, posteriori analysis is carried out for each possibility of monitoring data, and the optimal decision and posteriori analysis cost under each possibility of monitoring data are obtained based on the expected utility maximization theory; the cost model used is the same as that in step one, and the structural state probability model is obtained by updating the structural state probability model in step one through monitoring data and Bayesian theory; Step three, information value calculation: according to the future short-term monitoring data distribution predicted in step two, the mathematical expectation of the difference between the posteriori analysis cost and the prior analysis cost under each possibility of monitoring data is obtained to obtain the information value; then the optimal warning threshold under Bayesian posteriori analysis is obtained by maximizing the information value, which can ensure the maximum expected utility under the future monitoring data distribution; Step four, bridge structure warning: according to the structural reliability index, failure probability and failure risk function obtained through fatigue reliability analysis, and the optimal warning threshold obtained through information value analysis, warning judgment is carried out, and when the failure risk function value of a time period is higher than the optimal warning threshold, warning is carried out in the last time period; The step two is specifically: Step 2.1, predicting short-term future monitoring data distribution: based on the current monitoring data, the related parameters of the monitoring data distribution are updated through the Bayesian formula, and the updated data distribution is taken as the short-term future monitoring data distribution; Step 2.2, posteriori analysis: multiple samples are taken from the predicted short-term future monitoring data distribution, and posteriori analysis is carried out for each sample; the cost model used is consistent with the cost model in prior analysis, and the structural state probability model is updated by the Bayesian formula, as shown in the following formula: wherein, is a likelihood function, obtainable by structural condition monitoring data; Step 2.

3. Calculate the posterior analysis cost: For each data sample collected from the predicted monitoring data distribution, obtain the optimal posterior decision based on the expected utility theory and the corresponding posterior analysis cost The posterior analysis cost is calculated as follows: 。 2. The method of claim 1, wherein, The cost model is constructed in step one and specifically includes structural failure costs , structural repair costs , and structural operation costs ; The structural failure cost includes direct cost associated with structural damage and indirect cost due to loss of structural function; the structural repair cost includes cost of manpower and material required for repair and indirect cost due to structural repair; the structural operation cost includes economic loss due to regulatory measures; the structural failure cost and the structural repair cost are calculated as follows: wherein represents the economic loss due to structural failure, is the cost required for a single repair of the structure, is the discount rate, represents the time of the early warning; Operating costs The calculation of the operating costs can be dependent on the specific structure and scenario.

3. The method of claim 2, wherein, In step one, the structural state probability model is modeled as follows: based on the fatigue crack propagation theory, the structural fatigue reliability analysis is carried out to obtain the structural reliability index and failure probability within a certain time; the related formulas of the fatigue crack propagation theory are as follows: wherein, represents the fatigue crack depth; represents the number of cycles of the fatigue load; represents the fatigue crack depth at the nth cycle of the fatigue load; represents the fatigue crack depth at the nth cycle of the fatigue load; and are fatigue crack propagation constants, which can be determined by material testing; is a crack geometry correction factor; is an equivalent fatigue stress amplitude; for the convenience of fatigue reliability analysis, it is assumed that the value of the geometry correction factor is constant 1, so that the following formula can be integrated: wherein, represents the initial fatigue crack depth; represents the mean value of the number of load cycles, which can be determined at predetermined time intervals; represents the fatigue crack depth at time t; the fatigue limit state equation can be defined as: represents the fatigue crack depth at time t; the fatigue limit state equation can be defined as: wherein, is the limit threshold value of the fatigue crack; the HL-RF algorithm is used to solve the fatigue reliability. wherein, represents the iteration is carried out to the step; after the iteration is completed to obtain the final reliability index the structure failure probability can be calculated: The structural failure risk index can be further defined by the failure probability, so that the structural failure risk index is taken as the parameter representing the structural state, and the related formula is as follows: wherein, representing the time period is not failed and the probability of the time period being failed, is the structure failure risk function, and the value thereof can be used as a structure failure risk index.

4. The method of claim 3, wherein, The prior analysis cost calculated in step one is specifically: based on the cost model and the structure state probability model, the optimal prior decision is obtained based on the expected utility maximization theory and the corresponding prior analysis cost The prior analysis cost is calculated as shown in the following formula: wherein is a parameter affecting the structural state probability model, is the structural state probability model; denotes the total cost in the early warning decision process, which consists of the structural failure cost , the structural repair cost and the structural operation cost .

5. The method of claim 1, wherein, In step three, the information value is calculated as follows: based on the prior analysis cost obtained in step one, the posteriori analysis cost obtained in step two and the predicted monitoring data distribution, the information value is calculated, and the calculation formula of the information value is as follows: wherein represents the set of all possible structural monitoring data samples, i.e. the predicted monitoring data distribution.

6. The method of claim 5, wherein, The optimal early warning threshold is calculated in step three, which is different early warning thresholds will result in different early warning costs In order to obtain the highest early warning benefit, the early warning threshold is taken as the optimization variable, and the optimal early warning threshold is obtained by maximizing the information value That is: wherein, represents the optimal early warning threshold when the supplementary information sample set is In the structural early warning application scenario based on Bayesian decision, 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 equivalent to minimizing the expected value of the posterior analysis cost in the post-prior analysis, that is: 。 7. The method of claim 1, wherein, The step four is specifically: Step 4.1, according to the current monitoring data obtained under each time period structure reliability, failure probability and failure risk indicators to make the corresponding curve, and determine the best warning threshold interval; Step 4.2, determine the warning time: according to the failure risk index curve, when a time period of failure risk index value exceeds the warning threshold, the last time period as the warning time. 8.An electronic device comprising a memory and a processor, the memory storing a computer program, wherein, The processor executes the computer program to realize the steps of the method of any one of claims 1-7.

9. A computer readable storage medium for storing computer instructions, characterized in that, The computer instructions are executed by the processor to realize the steps of the method of any one of claims 1-7.

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