A bridge performance evaluation and early warning method based on influence lines

Abstract

The present invention discloses a bridge performance assessment and early warning method based on influence lines, comprising the following steps: obtaining the displacement influence line of the bridge through inspections with standard vehicles; obtaining evaluation indicators of the bridge status through the influence line, the evaluation indicators including at least one of a calibration coefficient, a decay coefficient, and an influence line similarity; real-time monitoring of heavy vehicles passing through the bridge to obtain the influence line and obtain an influence line envelope diagram; and predicting the maximum displacement that may occur in key sections of the bridge after the heavy vehicle passes through using the continuously updated influence line envelope diagram, which serves as the basis for timely early warning of the bridge. The present invention determines the health status of the bridge by establishing an influence line, and establishes a bridge displacement influence line envelope diagram by continuously monitoring the influence line after the heavy vehicle passes, predicting the maximum displacement that may occur in key locations of the bridge after the heavy vehicle passes, thereby achieving timely early warning of bridge displacement.

Description

Technical Field

[0001] The present invention relates to a bridge performance evaluation and early warning method, and in particular to an influence line-based bridge performance evaluation and early warning method. Technical Background

[0002] With the increasing number and age of bridges, the focus of bridge engineering has gradually shifted from construction to management, maintenance, and operation. As a vital component of transportation networks, bridge safety is crucial to the smooth flow of regional transportation networks and interregional economic exchange. Consequently, bridge health monitoring is gaining increasing attention. Bridge performance assessment and timely early warning are crucial components of bridge health monitoring. Regular bridge performance assessments are crucial for technicians to understand bridge conditions and provide guidance for the development of bridge maintenance plans. Furthermore, timely early warnings can provide early detection of potential risks, which is crucial for the safe operation and maintenance of bridges.

[0003] Traditional bridge performance assessment methods fall into several categories: visual inspection, mechanical analysis, non-destructive testing, and health monitoring indicator assessment. Visual inspection assesses the overall condition of a bridge by visually examining its appearance, structure, and components. Mechanical analysis requires modeling the bridge and performing force analysis and calculations to assess its load-bearing capacity. Non-destructive testing utilizes modern non-destructive testing technologies, such as ultrasonic testing and radar scanning, to inspect the bridge and obtain information about its internal structure to determine its safety. Health monitoring indicator assessment involves defining a series of bridge health indicators, such as crack density, corrosion severity, and vibration frequency, and then measuring and monitoring these indicators to assess the bridge's performance, safety, and remaining service life. These methods have certain drawbacks: they require experienced technicians; they consume significant time and manpower; they require the purchase of the latest testing equipment, which is prohibitively expensive; and they require the establishment of a standardized health monitoring system.

[0004] At present, to meet the demand for health monitoring of the large number and volume of national and provincial highway bridges, if a standardized monitoring system is used, it is necessary to configure a variety of monitoring sensors, including displacement, dynamic weighing and acceleration, which will incur a large amount of economic expenses. In order to control costs and accurately and quickly obtain evaluation information on the performance status of bridges, it is urgent to propose a lightweight monitoring system. Summary of the Invention

[0005] Purpose of the invention: In response to the defects of the existing technology, the present invention proposes a bridge performance evaluation and early warning method based on influence lines, which can accurately and quickly capture overweight vehicles passing through the bridge, obtain evaluation information on the bridge performance status, and save bridge operation and maintenance costs.

[0006] Technical solution: A bridge performance assessment and early warning method based on influence lines, including the following steps:

[0007] (1) For bridges equipped with displacement sensors, standard vehicle tests are used to obtain the displacement influence lines of key sections of the bridge. The specific contents include the following:

[0008] A w0-ton standard car passes through the bridge at a constant speed v, and the time it takes to pass is t;

[0009] The displacement sensor samples at a fixed sampling frequency f and collects the displacement response X=[x1,x2,...,x i ,...,x n ], where 1≤i≤n, and n=f·t;

[0010] The displacement response is converted into unit displacement using the following formula:

[0011]

[0012] where δ i Indicates the corresponding position is The unit displacement at Δ is approximated as the displacement influence line of a certain section of the bridge;

[0013] (2) Predict the maximum displacement of key bridge parts after heavy vehicles pass through based on the influence line:

[0014] N max =9.8×W·δ d =9.8×W·max{δ1,δ2,...,δ i ,...,δ n}

[0015] δ d =max{δ1,δ2,...,δ i ,...,δ n} represents the maximum unit displacement of the key part of the bridge after the standard vehicle passes through, and W represents the weight of the heavy vehicle;

[0016] Early warning is achieved based on the maximum displacement that may occur in key parts of the bridge.

[0017] In one embodiment, the bridge performance assessment and early warning method based on influence lines further includes the following steps:

[0018] (3) Using a dynamic weighing system, monitor the heavy vehicles passing through the bridge and update a bridge displacement influence line. By continuously monitoring the heavy vehicles, an envelope diagram of the bridge displacement influence line is obtained.

[0019] (4) The maximum displacement of key parts of the bridge after heavy vehicles pass through the displacement influence line envelope diagram to achieve early warning.

[0020] Specifically, step (3) includes the following:

[0021] (3.1) Suppose K heavy vehicles pass through a bridge of width L equipped with a dynamic weighing system. The dynamic weighing system records the time when the kth heavy vehicle passes as T k , the speed is v k , the weight of the heavy vehicle is w k The time it takes for the heavy vehicle to pass completely is t k , the travel speed remains unchanged, that is, t k =L / v k ;

[0022] (3.2) Record the same time T k , the time span is t k , the sampling signal of the displacement sensor with a sampling frequency of f, and the displacement response X k =[x1 k ,x2 k ,...,x i k ,...,x n k ], where n = f·t k ;

[0023] (3.3)Convert the displacement response into unit displacement:

[0024]

[0025] Among them, δ i k Indicates that the position corresponding to the k-th vehicle passing through the bridge is The unit displacement of the monitoring part caused by

[0026] A total of K unit displacements are obtained, namely Δ 1 ,Δ 2 ,...,Δ k ,...,Δ K , different matrices have different lengths;

[0027] (3.4) Fitting the K unit displacements with a continuous curve to obtain the envelope area of ​​the fitting curve. Preferably, a polynomial fitting method can be used to fit the K unit displacements, specifically including the following:

[0028] (3.4.1) Determine the order m;

[0029] (3.4.2) Assume that the polynomial is f(z;a)=a0+a1z+a2z 2 +…+a m z m , where a represents all the parameters to be determined a0, a1, a2, ..., am ;

[0030] (3.4.3) Calculate the square error function Derivative the square error function and set the derivative equal to zero to obtain the parameter a k equation, and obtain the parameter vector a k ^; where E k represents the square error function of the k-th unit displacement vector fitting curve;

[0031] (3.4.4) K unit displacement vectors are fitted to a total of K fitting curves, and the envelope of the fitting curve is obtained as Ω, that is,

[0032] Furthermore, the step (4) specifically includes the following contents:

[0033] Assume that on a long route, the dynamic weighing system has detected the passage of a heavy vehicle and recorded the weight W of the heavy vehicle;

[0034] The bridge predicts the maximum displacement of key parts after a heavy vehicle with a weight of W passes through the bridge based on the influence line envelope area:

[0035] N max =9.8×W·max(Ω)

[0036] Among them, N max It represents the maximum displacement that may occur in the key parts, and Ω represents the area of ​​the influence line envelope diagram.

[0037] In one embodiment, the bridge performance evaluation and early warning method based on the influence line further includes the step of obtaining various evaluation indicators of bridge performance according to the influence line, wherein the evaluation indicators include at least one of a calibration coefficient, a decay coefficient, and an influence line similarity;

[0038] Specifically, the calibration coefficient is calculated as follows:

[0039] Take the unit displacement δ of the key part of the bridge test s , take the maximum unit displacement δ after a standard vehicle passes through the key part of the bridge d =max{δ1,δ2,...,δ i ,...,δ n};

[0040] The calibration coefficient is defined as:

[0041]

[0042] when When , it indicates that the bridge performance is degraded.

[0043] The decay coefficient is calculated as follows:

[0044] The maximum unit displacement of the key position of the bridge obtained from the standard vehicle test last year is defined as The maximum unit displacement of the key position of the bridge obtained from the standard vehicle test this year is

[0045] The decay coefficient is defined as:

[0046]

[0047] When λ>1, it means that the stiffness of the bridge has declined.

[0048] The influence line similarity is calculated as follows:

[0049] Defining a vector and vector They represent the unit displacement of the same bridge at different times, which is approximately the displacement influence line of the bridge at different times;

[0050] Introducing the modal confidence criterion:

[0051]

[0052] Mac represents the influence line similarity, that is, the correlation of the displacement influence lines of the bridge at different periods.

[0053] Compared with the prior art, the present invention has the following significant improvements:

[0054] 1. The present invention regularly obtains the displacement influence line of the bridge through standard vehicle testing to obtain indicators such as calibration coefficient, decay coefficient and influence line similarity to evaluate bridge performance degradation, stiffness attenuation and determine whether the bridge has structural damage;

[0055] 2. For lightweight bridges, the present invention uses the influence lines obtained from standard vehicle tests to predict the maximum displacement that may occur in key parts of the bridge after heavy vehicle passage;

[0056] 3. For bridges equipped with dynamic weighing systems, the present invention monitors heavy vehicles and promptly obtains the displacement influence lines of the bridges. This is used to obtain the displacement influence line envelope diagram, which is then used to predict the maximum displacement that may occur at key parts of the bridge after the heavy vehicles pass through.

[0057] 4. The present invention can provide early warning for possible excessive displacement, and then notify the traffic management department to take corresponding measures in time to prevent major damage to the bridge and affect traffic safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1Flowchart of a bridge performance evaluation and early warning method based on influence lines in one embodiment. DETAILED DESCRIPTION

[0059] To make the above-mentioned objects, features, and advantages of the present application more clearly understood, the specific embodiments of the present application are described in detail below with reference to the accompanying drawings. The following description sets forth many specific details to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways than those described herein, and those skilled in the art can make similar improvements without violating the scope of the present application. Therefore, the present application is not limited to the specific embodiments disclosed below.

[0060] like Figure 1 As shown, a bridge performance evaluation and early warning method based on influence lines includes the following steps:

[0061] (1) Using an m-ton standard vehicle test, the displacement response of the bridges (with displacement sensors) along the national and provincial highways is obtained, and the displacement influence lines of the key sections of the bridges are obtained;

[0062] (2) Obtain various evaluation indicators of bridge performance based on the influence line; the evaluation indicators include but are not limited to calibration coefficient, decay coefficient, and influence line similarity;

[0063] (3) For bridges with only displacement sensors, the displacement influence lines obtained from standard vehicle tests are used to predict the maximum displacement of key parts of the bridge after a heavy vehicle passes through, thereby achieving early warning;

[0064] (4) Using a dynamic weighing system, monitor the heavy vehicles passing through the bridge and update a bridge displacement influence line. By continuously monitoring the heavy vehicles, an envelope diagram of the bridge displacement influence line is obtained.

[0065] (5) For bridges with dynamic weighing systems, the maximum displacement that may occur in key parts of the bridge after a heavy vehicle passes through is predicted through the displacement influence line envelope diagram, thereby completing the early warning of the bridge health monitoring system.

[0066] It should be noted that steps (1) and (3) are the most basic early warning schemes of the present invention, which can be implemented separately on bridges with only displacement sensors. On this basis, steps (4) and (5) can also be implemented for bridges with dynamic weighing systems. At the same time, the present invention can also calculate one or more evaluation indicators based on the influence line to pre-evaluate the performance of the bridge, i.e., step (2). The present invention does not limit the order or combination of the above steps. Those skilled in the art can adopt different combinations of steps or adjust the order of the steps according to the actual situation of the bridge to achieve different evaluation and early warning requirements.

[0067] This embodiment takes a 49-ton standard vehicle as an example to describe the specific contents of each step in detail.

[0068] The process of step (1) is as follows:

[0069] A 49-ton standard vehicle is used to pass through the bridge at a constant speed v, and the passing time is t. The displacement sensor in the monitoring system samples at a fixed sampling frequency f, and collects the displacement response X=[x1,x2,...,x i ,...,x n ], where 1≤i≤n, and n=f·t.

[0070] Convert the displacement response to unit displacement:

[0071] where δ i Indicates the corresponding position is The unit displacement at , that is, Δ can be approximately expressed as the displacement influence line of a certain section of the bridge.

[0072] In step (2), the calculation process of each evaluation index is as follows:

[0073] (2.1) Calibration coefficient

[0074] Take the unit displacement δ of the key part of the bridge test s , take the maximum unit displacement δ after a standard vehicle passes through the key part of the bridge d =max{δ1,δ2,...,δ i ,...,δ n}; The calibration coefficient is defined as:

[0075]

[0076] when When , it indicates that the bridge performance is degraded.

[0077] (2.2) Recession coefficient

[0078] Assume that the maximum unit displacement of the key position of the bridge obtained from the standard vehicle test last year is The maximum unit displacement of the key position of the bridge obtained from the standard vehicle test this year is The decay coefficient is defined as:

[0079]

[0080] When λ>1, it means that the stiffness of the bridge has declined.

[0081] (2.3) Influence line similarity

[0082] Assumption vector and vector They represent the unit displacement of the same bridge at different times, which are approximately the displacement influence lines of the bridge at different times.

[0083] Introducing the modal confidence criterion:

[0084]

[0085] Mac represents the correlation between two vectors and is used to determine whether a bridge has structural damage.

[0086] The closer Mac is to 1, the more correlated the two vectors are, or the more similar their mode shapes are. Conversely, a Mac close to 0 indicates that the two vectors are independent or dissimilar; this suggests a possible structural problem with the bridge, leading to significant differences in influence lines for the same bridge at different times.

[0087] The process of step (3) is as follows:

[0088] For bridges with only displacement sensors, the influence line obtained from the standard vehicle test can be used to predict the maximum displacement of key parts after a heavy vehicle with a weight of W passes through the bridge:

[0089] N max =9.8×W·δ d =9.8×W·max{δ1,δ2,…,δ i ,…,δ n}

[0090] where max{δ1,δ2,…,δ i ,…,δ n} comes from step (1).

[0091] The process of step (4) is as follows:

[0092] Suppose K heavy vehicles pass through a bridge with a width of L equipped with a dynamic weighing system. Assume that the dynamic weighing system records the time when the kth heavy vehicle passes as T k , the speed is v k , the weight of the heavy vehicle is w k The time it takes for the heavy vehicle to pass completely is t k , assuming the speed remains constant, that is, t k =L / v k .

[0093] Record at the same time T k , the time span is t k The sampling signal of the displacement sensor (the sampling frequency remains unchanged at f) is used to obtain the displacement response X k =[x1 k ,x2 k ,…,x ik ,…,x n k ], where n = f·t k .

[0094] Convert the displacement response to unit displacement:

[0095] where δ i k Indicates that the position corresponding to the k-th vehicle passing through the bridge is The unit displacement of the monitoring part is caused by . Therefore, a total of K one-dimensional matrices are obtained, which are Δ 1 ,Δ 2 ,…,Δ k ,…,Δ K (Different matrices have different lengths).

[0096] Use a polynomial to fit K unit displacements:

[0097] S1: Determine the order m;

[0098] S2: Assume the polynomial is f(z;a)=a0+a1z+a2z 2 +…+a m z m , where a represents all the parameters to be determined a0, a1, a2, ..., a m ;

[0099] S3: Calculate the squared error function Derivative the square error function and set the derivative equal to zero to obtain the parameter a k The equation of parameter vector a can be obtained k ^. Among them E k Represents the square error function of the k-th unit displacement vector fitting curve.

[0100] K unit displacement vectors are fitted to a total of K fitting curves, and the envelope area of ​​the fitting curve is obtained as Ω, that is,

[0101] The process of step (5) is as follows:

[0102] Assume that on a long line, the dynamic weighing system has detected the passage of a heavy vehicle and recorded the weight W of the heavy vehicle. For bridges with an influence line envelope diagram available, the maximum displacement N of the key parts that may occur after a heavy vehicle with a weight of W passes through the bridge can be predicted based on the area Ω of the influence line envelope diagram. max :

[0103] N max =9.8×W·max(Ω).

[0104] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0105] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A bridge performance evaluation and early warning method based on influence lines, characterized in that: The steps include: (1) For bridges equipped with displacement sensors, standard vehicle tests are used to obtain the displacement influence lines of key sections of the bridge. The specific contents include the following: A standard car with a ω0 ton capacity passes through the bridge at a constant speed v, and the time it takes to pass is t; The displacement sensor samples at a fixed sampling frequency f and collects the displacement response X=[x1,x2,...,x i ,...,x n ], where 1≤i≤n, and n=f·t; The displacement response is converted into unit displacement using the following formula: where δ i Indicates the corresponding position is The unit displacement at Δ is approximated as the displacement influence line of a certain section of the bridge; (2) Predict the maximum displacement of key bridge parts after heavy vehicles pass through based on the influence line: N max =9.8×W·δ d =9.8×W·max{δ1,δ2,…,δ i ,…,d n } δ d =max{δ1,δ2,…,δ i ,...,δ n } represents the maximum unit displacement of the key part of the bridge after the standard vehicle passes through, W represents the mass of the heavy vehicle, the unit is kg; Provide early warning based on the maximum possible displacement of key bridge parts; (3) Using a dynamic weighing system, monitor the heavy vehicle passing through the bridge, update a bridge displacement influence line, and obtain the bridge displacement influence line envelope diagram by continuously monitoring the heavy vehicle; specifically, the following contents are included: (3.1) Suppose K heavy vehicles pass through a bridge of width L equipped with a dynamic weighing system. The dynamic weighing system records the time when the kth heavy vehicle passes as T k , the speed is v k , mass is w k , the unit is kg, the time it takes for the heavy vehicle to pass completely is t k , the travel speed remains unchanged, that is, t k =L / v k ; (3.2) Record the same time T k , the time span is t k , the sampling signal of the displacement sensor with a sampling frequency of f, and the displacement response X k =[x1 k ,x2 k ,...,x i k ,...,x n k ], where n = f·t k ; (3.3)Convert the displacement response into unit displacement: Among them, δ i k Indicates that the position corresponding to the k-th vehicle passing through the bridge is The unit displacement of the monitoring part caused by A total of K unit displacements are obtained, namely Δ 1 ,Δ 2 ,...,Δ k ,…,Δ K , different matrices have different lengths; (3.4) Use a continuous curve to fit K unit displacements and obtain the envelope area of ​​the fitting curve; (4) The maximum displacement of key parts of the bridge after heavy vehicles pass through the displacement influence line envelope diagram to achieve early warning.

2. The bridge performance evaluation and early warning method based on influence line according to claim 1 is characterized in that: In the step (3.4), a polynomial fitting method is used to fit K unit displacements, specifically including the following contents: (3.4.1) Determine the order m; (3.4.2) Assume that the polynomial is f(z;a)=a0+a1z+a2z 2 +…+a m z m , where a represents all the parameters to be determined a0, a1, a2, ..., a m ; (3.4.3) Calculate the square error function Derivative the square error function and set the derivative equal to zero to obtain the parameter a k equation, and obtain the parameter vector a k^ ; Among them E k represents the square error function of the k-th unit displacement vector fitting curve; (3.4.4) K unit displacement vectors are fitted to a total of K fitting curves, and the envelope of the fitting curve is obtained as Ω, that is, 3. The bridge performance evaluation and early warning method based on influence line according to claim 1 is characterized in that: The step (4) specifically includes the following contents: Assume that on a long route, the dynamic weighing system has detected the passage of a heavy vehicle and recorded the mass W of the heavy vehicle in kg; The bridge predicts the maximum displacement of key parts after a heavy vehicle with mass W passes through the bridge based on the influence line envelope area: N max =9.8×W·max(Ω) Among them, N max It represents the maximum displacement that may occur in the key parts, and Ω represents the area of ​​the influence line envelope diagram.

4. The bridge performance evaluation and early warning method based on influence line according to claim 1 is characterized in that: The method further includes the step of obtaining various evaluation indicators of bridge performance according to the influence line, wherein the evaluation indicators include at least one of a calibration coefficient, a decay coefficient, and an influence line similarity.

5. The bridge performance evaluation and early warning method based on influence line according to claim 4 is characterized in that: The calibration coefficient is calculated as follows: Take the unit displacement δ of the key part of the bridge test s , take the maximum unit displacement δ after a standard vehicle passes through the key part of the bridge d =max{δ1,δ2,...,δ i ,…,δ n }; The calibration coefficient is defined as: when When , it indicates that the bridge performance is degraded.

6. The bridge performance evaluation and early warning method based on influence line according to claim 4 is characterized in that: The decay coefficient is calculated as follows: The maximum unit displacement of the key position of the bridge obtained from the standard vehicle test last year is defined as The maximum unit displacement of the key position of the bridge obtained from the standard vehicle test this year is The decay coefficient is defined as: When λ>1, it means that the stiffness of the bridge has declined.

7. The bridge performance evaluation and early warning method based on influence line according to claim 4 is characterized in that: The influence line similarity is calculated as follows: Defining a vector and vector They represent the unit displacement of the same bridge at different times, which is approximately the displacement influence line of the bridge at different times; Introducing the modal confidence criterion: Mac represents the influence line similarity, that is, the correlation of the displacement influence lines of the bridge at different periods.

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