A method and system for setting early warning thresholds for health monitoring of large-span arch bridges based on reliability criteria

Abstract

The present invention discloses a method and system for setting a health monitoring warning threshold for a large-span arch bridge based on a reliability criterion, which relates to the technical field of arch bridges, including establishing a function function according to the structural limit response and warning threshold of the large-span arch bridge; determining a target reliability index, and setting a random variable, an initial value of the warning threshold, and a convergence tolerance error; calculating the gradient value of the function function, calculating a scaling factor according to the gradient value, obtaining the failure point of the function function through the scaling factor combined with a conjugate search strategy, and updating the warning threshold of the failure point; continuously iterating until the error is less than or equal to the convergence tolerance error, establishing a reliability criterion for setting the warning threshold, and obtaining the warning threshold of the reliability index of the target to be measured according to the reliability criterion. Based on the function function of the large-span arch bridge, the present invention establishes a connection between the structural reliability level and the service status, inverts the corresponding warning threshold, proposes a reliability criterion, and accurately and reliably sets the warning threshold of the large-span arch bridge.

Description

Technical Field

[0001] The present invention relates to the technical field of arch bridges, and more particularly to a method and system for setting health monitoring and early warning thresholds for a long-span arch bridge based on a reliability criterion. Background Art

[0002] Due to its significant advantages such as high structural rigidity, good economy and strong adaptability in mountainous areas, long-span arch bridges have become an important type of bridge for transportation networks across mountains and canyons. However, with the increase in service life, long-span arch bridges will inevitably experience performance degradation under the combined effects of multiple factors such as environmental erosion and heavy traffic. Therefore, setting a reasonable warning threshold is of great significance for effectively judging the operating status of the structure and realizing the accurate warning function of the arch bridge health monitoring system.

[0003] At present, the warning thresholds for arch bridges can be divided into two categories, namely, the warning thresholds based on monitoring data and the warning thresholds based on finite element models. The warning thresholds based on monitoring data determine the change range of the structural monitoring indicators in the short term by analyzing the statistical laws of the monitoring data, and then set the warning thresholds. The warning thresholds based on monitoring data can provide a good reference for low-level warnings, but due to the data-driven nature of such methods, the warning thresholds are only related to the data features, and are not strongly related to the structural status, resulting in low threshold reliability and easy misjudgment.

[0004] The warning threshold based on the finite element model is mainly combined with the design code limit or the finite element calculation analysis under the design load to calculate the safety limit reflecting the structural limit state. However, in the design stage, all types of loads are taken in the most unfavorable state, and a certain redundancy reserve is considered. The threshold setting includes human experience factors, which may cause the warning threshold to be too large. Excessive limits may lead to missed reports, endangering the safe operation of the structure.

[0005] In summary, how to accurately and reliably set the warning threshold of a long-span arch bridge has become a problem that technical personnel in this field urgently need to solve. Summary of the invention

[0006] In view of this, the present invention provides a method and system for setting health monitoring warning thresholds for large-span arch bridges based on the reliability criterion. Based on the functional function of the large-span arch bridge, the connection between the structural reliability level and the service status is established. The corresponding warning threshold is inverted by the target reliability index, and a reliability criterion for setting the warning threshold is proposed, so that the warning threshold of the large-span arch bridge is set accurately and reliably.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] A method for setting health monitoring early warning thresholds for a long-span arch bridge based on reliability criteria, comprising:

[0009] S1: Establish a functional function based on the structural limit response and warning threshold of the long-span arch bridge;

[0010] S2: Determine a target reliability index, and set a random variable, an initial value of a warning threshold, and a convergence tolerance according to the target reliability index;

[0011] S3: Calculate the gradient value of the functional function according to the random variable and the initial value of the warning threshold, further calculate the scaling factor according to the gradient value, and obtain the failure point of the functional function by combining the scaling factor with the conjugate search strategy;

[0012] S4: updating the warning threshold of the failure point;

[0013] S5: Repeat S3 and S4 until the iteration error is less than or equal to the convergence allowable error, and output the final warning threshold of the failure point;

[0014] S6: Establishing a reliability criterion for setting the warning threshold value so that a linear relationship is satisfied between the target reliability index and the warning threshold value, and obtaining the warning threshold value of the reliability index of the target to be measured according to the reliability criterion.

[0015] Preferably, the functional functions established in S1 specifically include:

[0016]

[0017] in, represents the functional function, u is a multidimensional random variable that affects the structural resistance; y R (u) is the ultimate response of the structure; is the warning threshold of the structural response.

[0018] Preferably, S3 specifically includes:

[0019] S301: Calculate the functional function at point The gradient value at k is the initial value of the random variable, is the initial value of the warning threshold;

[0020] S302: Calculate a scaling factor according to the gradient value, and the specific formula is as follows;

[0021]

[0022] S303: Calculating a conjugate search direction vector according to the scaling factor;

[0023]

[0024] S304: Calculating a recursive checkpoint according to the conjugate search direction vector;

[0025]

[0026] S305: Calculating a unit search direction vector according to the recursive checkpoint;

[0027]

[0028] S306: performing inverse reliability analysis, and calculating the failure point of the functional function according to the unit search direction vector and the target reliability index β;

[0029]

[0030] Among them, θ k is the scaling factor, is the gradient value of the functional function, p k is the conjugate search direction vector, is the recursive checkpoint along the conjugate search direction, λ k is a finite step length, u k+1 The failure point of the function.

[0031] Preferably, the S4 specifically includes:

[0032] S401: Set the function at point About Taylor series expansion of ;

[0033]

[0034] S402: Update the warning threshold as follows;

[0035]

[0036] Preferably, S5 specifically includes judging whether the iteration satisfies the convergence condition according to the following formula:

[0037]

[0038] Here, ε is the convergence tolerance.

[0039] Preferably, the S6 specifically includes:

[0040] S601, establishing a reliability criterion for setting a warning threshold value, so that a linear relationship is satisfied between the target reliability index and the warning threshold value;

[0041] S602: Calculate the warning thresholds corresponding to any two target reliability indicators β1 and β2 (β1 < β2) and

[0042] S603: According to the linear relationship, determine the warning threshold value under the reliability index of the target to be measured by interpolation according to the following formula

[0043] A long-span arch bridge health monitoring early warning threshold setting system based on reliability criteria, comprising:

[0044] Function establishment module, which establishes the function according to the structural limit response and warning threshold of the long-span arch bridge;

[0045] An indicator establishment module determines a target reliability indicator and sets a random variable, an initial value of a warning threshold, and a convergence tolerance according to the target reliability indicator;

[0046] A failure point calculation module calculates the gradient value of the functional function according to the random variable and the initial value of the warning threshold, further calculates the scaling factor according to the gradient value, and obtains the failure point of the functional function by combining the scaling factor with a conjugate search strategy;

[0047] A failure point update module, which updates the warning threshold of the failure point;

[0048] An iterative update module, which repeats the operations of the failure point calculation module and the failure point update module until the iteration error is less than or equal to the convergence allowable error, and outputs the final warning threshold of the failure point;

[0049] The warning threshold calculation module establishes a reliability criterion for setting the warning threshold so that a linear relationship is satisfied between the target reliability index and the warning threshold, and obtains the warning threshold of the reliability index of the target to be measured according to the reliability criterion.

[0050] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a method and system for setting health monitoring warning thresholds for large-span arch bridges based on the reliability criterion. Based on the functional function of the large-span arch bridge, the connection between the structural reliability level and the service status is established. The corresponding warning threshold is inverted by the target reliability index, and a reliability criterion for setting the warning threshold is proposed. The warning threshold under any reliability index is obtained by means of interpolation, so that the threshold setting is well-founded and relatively objective, and can effectively realize the fine setting of the warning threshold and the accurate warning of the structural performance, overcome the problem of strong subjectivity in the existing threshold setting, and avoid the underreporting phenomenon that often occurs in the health monitoring system. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0052] Figure 1 The accompanying drawing is a flow chart of the method steps provided by the present invention;

[0053] Figure 2 The accompanying drawing is a schematic diagram of the layout of a large-span top-decker reinforced concrete arch bridge for rapid evaluation provided by the present invention;

[0054] Figure 3 The accompanying drawing is a schematic diagram of the linear relationship between the target reliability index and the warning threshold provided by the present invention. DETAILED DESCRIPTION

[0055] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] The embodiment of the present invention discloses a method for setting a health monitoring warning threshold of a long-span arch bridge based on a reliability criterion. Figure 1 As shown, including:

[0057] S1: Establish a functional function based on the structural limit response and warning threshold of the long-span arch bridge;

[0058] S2: Determine the target reliability index, and set the random variable, the initial value of the warning threshold and the convergence tolerance according to the target reliability index;

[0059] S3: Calculate the gradient value of the functional function according to the initial value of the random variable and the warning threshold, further calculate the scaling factor according to the gradient value, and obtain the failure point of the functional function by combining the scaling factor with the conjugate search strategy;

[0060] S4: Update the warning threshold of the failure point;

[0061] S5: Repeat S3 and S4 until the iteration error is less than or equal to the convergence tolerance error, and output the final warning threshold of the failure point;

[0062] S6: Establish a reliability criterion for setting the warning threshold so that the target reliability index and the warning threshold satisfy a linear relationship, and obtain the warning threshold of the reliability index of the target to be measured according to the reliability criterion.

[0063] In a specific embodiment, the functional function established in S1 specifically includes:

[0064]

[0065] in, represents the functional function, u is a multidimensional random variable that affects the structural resistance; y R (u) is the ultimate response of the structure; is the warning threshold of the structural response.

[0066] In a specific embodiment, the target reliability index is represented by β, and the initial value of the random variable u k The average value and initial value of the warning threshold can be taken It can be 0, and the convergence tolerance ε can be 10 -3 .

[0067] In a specific embodiment, S3 specifically includes:

[0068] S301: Calculate the function at point The gradient value at k is the initial value of the random variable, is the initial value of the warning threshold;

[0069] S302: Calculate the scaling factor according to the gradient value. The specific formula is as follows;

[0070]

[0071] S303: Calculate a conjugate search direction vector according to the scaling factor;

[0072]

[0073] S304: Calculate a recursive checkpoint according to a conjugate search direction vector;

[0074]

[0075] S305: Calculate the unit search direction vector according to the recursive checkpoint;

[0076]

[0077] S306: performing inverse reliability analysis, calculating the failure point of the functional function according to the unit search direction vector and the target reliability index β;

[0078]

[0079] Among them, θ k is the scaling factor, is the gradient value of the functional function, p k is the conjugate search direction vector, is the recursive checkpoint along the conjugate search direction, λ k is a finite step length, u k+1 The failure point of the function.

[0080] In a specific embodiment, S4 specifically includes:

[0081] S401: Set the function at point About Taylor series expansion of ;

[0082]

[0083] S402: Update the warning threshold as follows;

[0084]

[0085] In a specific embodiment, S5 specifically includes judging whether the iteration satisfies the convergence condition according to the following formula:

[0086]

[0087] Here, ε is the convergence tolerance.

[0088] In a specific embodiment, S6 specifically includes:

[0089] S601, establishing a reliability criterion for setting the warning threshold (i.e., a linear relationship is satisfied between the target reliability index and the warning threshold), so that a linear relationship is satisfied between the target reliability index and the warning threshold;

[0090] S602: Calculate the warning thresholds corresponding to any two target reliability indicators β1 and β2 (β1 < β2) and

[0091] S603: According to the linear relationship, determine the warning threshold value under the reliability index of the target to be measured by interpolation according to the following formula

[0092] A long-span arch bridge health monitoring early warning threshold setting system based on reliability criteria, comprising:

[0093] Function establishment module, which establishes the function according to the structural limit response and warning threshold of the long-span arch bridge;

[0094] The indicator establishment module determines the target reliability indicator and sets the initial value of the random variable, the warning threshold and the convergence tolerance according to the target reliability indicator;

[0095] The failure point calculation module calculates the gradient value of the functional function according to the initial value of the random variable and the warning threshold, further calculates the scaling factor according to the gradient value, and obtains the failure point of the functional function through the scaling factor combined with the conjugate search strategy;

[0096] Failure point update module, updates the warning threshold of failure points;

[0097] The iterative update module repeats the operations of the failure point calculation module and the failure point update module until the iteration error is less than or equal to the convergence allowable error, and outputs the final warning threshold of the failure point;

[0098] The warning threshold calculation module establishes a reliability criterion for setting the warning threshold so that the target reliability index and the warning threshold satisfy a linear relationship, and obtains the warning threshold of the reliability index of the target to be tested according to the reliability criterion. Specific embodiment 1

[0100] In order to further explain in detail the method for setting the early warning threshold of a large-span arch bridge based on the reliability criterion of the present invention, Figure 2 Taking the large-span top-supported reinforced concrete arch bridge shown in the figure as an example, a specific rapid evaluation operation and result verification of the service status of the bridge are carried out, such as Figure 2 As shown, the main arch axis of the bridge used in this embodiment adopts a catenary, with a calculated span of 600m, a rise of 125m, a rise-span ratio of f / l=1 / 4.8, an arch axis coefficient of m=1.9, and a single-box single-chamber variable height section. The arch top section is 8m high, the arch foot section is 12m high, and the width is 6.5m. The lateral center distance of the arch rib is 16.5m. Two ribs of the beam are arranged horizontally, in the form of parallel arches. The concrete arch rib adopts a steel tube concrete truss structure as a rigid skeleton. The outer diameter of the truss upper chord tube is 900mm, and the wall thickness of the steel tube changes from 30mm to 35mm from the arch foot to the arch top. The outer diameter of the lower chord tube is 900mm, and the wall thickness changes from 35mm to 30mm from the arch foot to the arch top. The steel material is Q420qD25Z. The external concrete of the arch rib adopts C60, and C80 self-compacting micro-expansive concrete is poured into the main chord tube.

[0101] The long-span arch bridge warning threshold setting of this embodiment adopts the following steps:

[0102] S1. Establish the functional function of the long-span arch bridge;

[0103] Through the ultimate response analysis of long-span arch bridges, the mid-span section function can be expressed as The random variables include the amplitude of arch axis deviation, uniform temperature change of arch rib, non-uniform temperature change of arch rib, section ultimate bending moment and section ultimate axial force. The statistical characteristics of each random variable are shown in Table 1.

[0104] Table 1 Random variables and their statistical parameters

[0105] random variable Distribution Type Mean Standard Deviation Arch axis deviation amplitude β(m) normal distribution 0 L / 3000 Uniform temperature change of arch rib (t1+t2) (℃) normal distribution 20 4 Uneven temperature change of arch rib (t1-t2) (℃) normal distribution 5 1 Section ultimate bending moment Mu (kN·m) normal distribution Design value 0.3 times design value Section ultimate axial force Nu (kN) normal distribution Design value 0.2 times design value

[0106] S2, determine the target reliability index, set the initial value of the random variable, the warning threshold and the convergence tolerance;

[0107] For the target reliability index β=5, set the initial value of failure point u0=[0,0,0,0,0] and the initial value of response limit Step size λ k ≡1.2, allowable error ε=10 -3 .

[0108] S3, using a conjugate search strategy to obtain the failure point of the functional function;

[0109] Calculate the function at the point The gradient value at:

[0110]

[0111] Compute the conjugate search direction vector:

[0112]

[0113] Compute recursive checkpoints:

[0114]

[0115] Compute the unit search direction vector:

[0116]

[0117] Calculate the failure point of the function:

[0118] u1=[-2.5352,1.5374,0.1639,-1.2329,-3.8291];

[0119] S4, updating the warning threshold at the failure point;

[0120] Since the gradient of the performance function to the warning threshold is -1, and at point The function value at is 0.6826m. Therefore, we can get:

[0121]

[0122] S5, repeat steps S3 and S4 until the convergence condition is met, and output the warning threshold corresponding to the target reliability index;

[0123] At this time, the iteration error is 0.9822, which is greater than the allowable error. Therefore, it is necessary to continue iteration and repeat steps S3 and S4 to obtain the warning threshold corresponding to the target reliability index of 0.835m.

[0124] S6. Establish a reliability criterion for setting the warning threshold to achieve the acquisition of the warning threshold under any target reliability index.

[0125] S601, establishing a reliability criterion for setting the warning threshold, that is, a linear relationship is satisfied between the target reliability index and the warning threshold;

[0126] The warning thresholds corresponding to different reliability indicators are calculated, such as Figure 3 As shown. Figure 3 It can be seen that there is a basically linear relationship between the target reliability index and the warning threshold, so the reliability criterion for setting the warning threshold can be established.

[0127] S602: Calculate the warning thresholds corresponding to any two target reliability indicators β1 and β2 (β1 < β2) and

[0128] In addition, when the target reliability index β=2, the warning threshold is 1.171m.

[0129] S603, determine the warning threshold under the specified target reliability index by interpolation according to the following formula:

[0130] Through interpolation, the warning thresholds corresponding to other target reliability indicators can be quickly calculated. For example, when β = 3.5:

[0131]

[0132] In summary, the present invention discloses a method for setting health monitoring warning thresholds for large-span arch bridges based on reliability criteria. Based on the functional function of the large-span arch bridge, the connection between the structural reliability level and the service status is established. The warning threshold corresponding to the target reliability index is inverted, and a reliability criterion for setting the warning threshold is proposed. The warning threshold under any reliability index is obtained by interpolation, so that the threshold setting is well-founded and relatively objective, and can effectively realize the fine setting of the warning threshold and the accurate warning of the structural performance, thus overcoming the problem of strong subjectivity in the existing threshold setting and avoiding the underreporting phenomenon that often occurs in the health monitoring system.

[0133] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0134] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for setting early warning thresholds for health monitoring of large-span arch bridges based on reliability criteria, characterized in that: include: S1: Establish a functional function based on the structural limit response and warning threshold of the long-span arch bridge; S2: Determine a target reliability index, and set a random variable, an initial value of a warning threshold, and a convergence tolerance according to the target reliability index; S3: Calculate the gradient value of the functional function according to the random variable and the initial value of the warning threshold, further calculate the scaling factor according to the gradient value, and obtain the failure point of the functional function by combining the scaling factor with the conjugate search strategy; The S3 specifically includes: S301: Calculate the functional function at point The gradient value at , where is the initial value of the random variable, is the initial value of the warning threshold; S302: Calculate a scaling factor according to the gradient value, and the specific formula is as follows; ； S303: Calculating a conjugate search direction vector according to the scaling factor; ； S304, calculating a recursive checkpoint according to the conjugate search direction vector; ； S305, calculating a unit search direction vector according to the recursive checkpoint; ； S306, perform inverse reliability analysis, according to the unit search direction vector and the target reliability index Calculate the failure point of the functional function; ； in, is the scaling factor, is the gradient value of the functional function, is the conjugate search direction vector, is the recursive checkpoint along the conjugate search direction, is a finite step length, is the failure point of the function; S4: updating the warning threshold of the failure point; S5: Repeat S3 and S4 until the iteration error is less than or equal to the convergence allowable error, and output the final warning threshold of the failure point; S6: Establishing a reliability criterion for setting the warning threshold value so that the target reliability index and the warning threshold value satisfy a linear relationship, and obtaining the warning threshold value of the reliability index of the target to be measured according to the reliability criterion.

2. According to the method for setting the health monitoring warning threshold of a large-span arch bridge based on the reliability criterion of claim 1, it is characterized in that: The functional functions established in S1 specifically include: ； in, represents the functional function, u is a multidimensional random variable that affects the structural resistance; is the ultimate response of the structure; is the warning threshold of the structural response.

3. According to the method for setting the health monitoring warning threshold of a long-span arch bridge based on the reliability criterion in claim 1, it is characterized in that: The S4 specifically includes: S401: Set the function at point About Taylor series expansion of ; ； S402: Update the warning threshold as follows; 。 4. According to the method for setting the health monitoring warning threshold of a long-span arch bridge based on the reliability criterion of claim 3, it is characterized in that: The S5 specifically includes judging whether the iteration meets the convergence condition according to the following formula: ； in, is the convergence tolerance.

5. According to the method for setting the health monitoring warning threshold of a long-span arch bridge based on the reliability criterion of claim 1, it is characterized in that: The S6 specifically includes: S601, establishing a reliability criterion for setting a warning threshold value, so that a linear relationship is satisfied between the target reliability index and the warning threshold value; S602. Calculate any two target reliability indicators and , ; The corresponding warning threshold and ; S603: According to the linear relationship, determine the warning threshold value under the reliability index of the target to be measured by interpolation according to the following formula .

6. A long-span arch bridge health monitoring warning threshold setting system based on reliability criteria, characterized in that: include: Function establishment module, which establishes the function according to the structural limit response and warning threshold of the long-span arch bridge; An indicator establishment module determines a target reliability indicator and sets a random variable, an initial value of a warning threshold, and a convergence tolerance according to the target reliability indicator; A failure point calculation module calculates the gradient value of the functional function according to the random variable and the initial value of the warning threshold, further calculates the scaling factor according to the gradient value, and obtains the failure point of the functional function by combining the scaling factor with a conjugate search strategy; The failure point calculation module specifically includes: Calculate the power function at the point The gradient value at , where is the initial value of the random variable, is the initial value of the warning threshold; The scaling factor is calculated according to the gradient value, and the specific formula is as follows: ； Calculating a conjugate search direction vector according to the scaling factor; ； Calculating a recursive checkpoint according to the conjugate search direction vector; ； Calculating a unit search direction vector according to the recursive checkpoint; ； Perform inverse reliability analysis based on the unit search direction vector and the target reliability index Calculate the failure point of the functional function; ； in, is the scaling factor, is the gradient value of the functional function, is the conjugate search direction vector, is the recursive checkpoint along the conjugate search direction, is a finite step length, is the failure point of the function; A failure point update module, which updates the warning threshold of the failure point; An iterative update module, which repeats the operations of the failure point calculation module and the failure point update module until the iteration error is less than or equal to the convergence allowable error, and outputs the final warning threshold of the failure point; The warning threshold calculation module establishes a reliability criterion for setting the warning threshold so that a linear relationship is satisfied between the target reliability index and the warning threshold, and obtains the warning threshold of the reliability index of the target to be measured according to the reliability criterion.

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