Method and system for determining the influence line of a pc track beam and storage medium

Abstract

The application discloses a PC track beam influence line determination method and system and a storage medium. The method comprises the following steps: firstly, obtaining response data of a train passing through a PC track beam; then, determining a train position fitting model through linear fitting according to the collection time corresponding to a wave trough in the response data and train parameters; finally, solving the influence line based on the train position fitting model to obtain the PC track beam influence line. The PC track beam influence line determination method, system and storage medium are used for determining the vehicle position on the PC track beam by using the bridge response data, so that high-precision positioning devices and clock synchronization devices do not need to be additionally purchased, and the positioning and synchronization costs in the influence line determination process are reduced.

Description

Technical Field

[0001] This invention relates to the field of mechanical parameter or variable design technology, specifically to a method, system and storage medium for determining the influence line of a PC track beam. Background Technology

[0002] Straddle-type monorails have become the preferred solution for urban rail transit in large, medium, and small cities due to their low cost and high adaptability to complex environments. As the main load-bearing structure of straddle-type monorails, PC track beams inevitably suffer damage during long-term use due to material aging and load effects, leading to a decrease in the bridge's load-bearing capacity and durability, and in severe cases, threatening traffic safety. Influence lines are an inherent characteristic of PC track bridges. Due to their clear physical meaning and rich local bridge information, they have been successfully applied in damage identification and condition assessment. However, the prerequisite for realizing these applications is that the influence lines of the PC track beams can be obtained quickly and accurately.

[0003] Depending on the vehicle speed, influence line determination methods can be divided into static determination and dynamic determination. Static determination involves placing a loaded vehicle stationary at a designated location on the bridge and measuring the bridge response. Influence lines are then solved using several equations. While the method is simple to extract, the testing is time-consuming and labor-intensive, limiting its practical engineering application. Dynamic determination involves allowing vehicles to pass over the bridge at operating or normal speeds and measuring the bridge response. Influence lines are identified using vehicle position information, synchronization information, and bridge response information through matrix solving. Although influence line extraction is complex, this method has less impact on traffic and has received widespread attention.

[0004] In recent years, some research has been conducted both domestically and internationally on the dynamic determination of influence lines. Existing research focuses on highway bridges, with limited application studies on rail bridges. On highway bridges, the vehicles loaded are typically two- or three-axle trucks. In contrast, rail trains have many more axles; a typical six-car rail train has 24 axles, increasing matrix ill-conditioning in the influence line solution process and thus affecting accuracy. Furthermore, influence line determination requires measuring vehicle position information and synchronizing this information with the bridge response. The mainstream approach is to purchase high-precision vehicle positioning equipment and clock servers. Compared to strain sensors and deflection measurement equipment, high-precision vehicle positioning equipment and clock servers are significantly more expensive, typically accounting for over 60% of the measurement cost, severely hindering large-scale engineering applications. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method, system, and storage medium for determining the influence line of PC track beams. This can reduce the positioning and synchronization costs during influence line determination. The specific technical solution is as follows:

[0006] Firstly, a method for determining the influence line of a PC track beam is provided, including:

[0007] Obtain response data of the train passing over the PC track beam;

[0008] Based on the acquisition time and train parameters corresponding to the troughs in the response data, a train position fitting model is determined by linear fitting.

[0009] Based on the train position fitting model, the vehicle load matrix is ​​constructed to solve for the influence line, thus obtaining the influence line of the PC track beam.

[0010] In conjunction with the first aspect, in a first possible implementation of the first aspect, the response data includes dynamic displacement response data or dynamic strain response data.

[0011] In conjunction with the first aspect, in the second possible implementation of the first aspect, the vehicle load matrix is ​​constructed using an interpolation method based on the train position fitting model.

[0012] In conjunction with the first aspect, in the third feasible method of the first aspect, the least squares method is used to solve for the influence line.

[0013] In a second aspect, a storage medium is provided that stores a computer program, which, when executed, implements the PC track beam influence line determination method as described in the first aspect and any of the first to third implementable methods of the first aspect.

[0014] Thirdly, a system for determining the influence line of a PC track beam is provided, including:

[0015] The acquisition module is configured to acquire response data of the train passing over the PC track beam;

[0016] The fitting module is configured to determine the train position fitting model by linear fitting based on the acquisition time and train parameters corresponding to the troughs in the response data.

[0017] The solution module is configured to construct the vehicle load matrix based on the train position fitting model and solve for the influence line to obtain the PC track beam influence line.

[0018] In conjunction with the fourth aspect, in the first possible implementation of the fourth aspect, the response data acquired by the acquisition module includes dynamic displacement response data or dynamic strain response data.

[0019] In conjunction with the fourth aspect, in the second possible implementation of the fourth aspect, the solution module includes:

[0020] The construction unit is configured to construct a vehicle load matrix based on the train position fitting model;

[0021] The solution unit is configured to solve for the influence line by constructing the vehicle load matrix, thereby obtaining the influence line of the PC track beam.

[0022] In conjunction with the second feasible method of the fourth aspect, in the third feasible method of the fourth aspect, the construction unit constructs the vehicle load matrix based on the train position fitting model using an interpolation method.

[0023] In conjunction with the second feasible method of the fourth aspect, in the fourth feasible method of the fourth aspect, the solving unit uses the least squares method to solve for the influence line.

[0024] Beneficial effects: The PC track beam influence line determination method, system and storage medium of the present invention determine the vehicle position on the PC track beam by using bridge response data, thus eliminating the need to purchase additional high-precision positioning devices and clock synchronization devices, reducing the positioning and synchronization costs in the influence line determination process. Attached Figure Description

[0025] To more clearly illustrate the specific embodiments of the present invention, the accompanying drawings used in the specific embodiments will be briefly described below. In all the drawings, the elements or parts are not necessarily drawn to scale.

[0026] Figure 1 This is a flowchart of a method for determining the influence line of a PC track beam according to an embodiment of the present invention;

[0027] Figure 2 This is a system block diagram of a PC track beam influence line measurement system provided in an embodiment of the present invention;

[0028] Figure 3 This is a schematic diagram showing the sensor's installation location;

[0029] Figure 4 This is a schematic diagram of the train load.

[0030] Figure 5 This is a diagram showing the strain response of the PC track beam at mid-span when a train passes.

[0031] Figure 6 This is a schematic diagram of the fitted train position curve;

[0032] Figure 7 This is a schematic diagram showing the results of the strain influence line determination at mid-span of the PC track beam. Detailed Implementation

[0033] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0034] like Figure 1 The flowchart shown illustrates the method for determining the influence line of a PC track beam. This method includes:

[0035] Step 1: Obtain the response data of the train passing over the PC track beam;

[0036] Step 2: Based on the acquisition time and train parameters corresponding to the troughs in the response data, determine the train position fitting model through linear fitting;

[0037] Step 3: Based on the train position fitting model, construct the vehicle load matrix and solve for the influence line to obtain the PC track beam influence line.

[0038] Specifically, the measurement method consists of three main steps. The first step is to acquire response data of the train passing over the PC track beam. To acquire this response data, such as... Figure 3 As shown, a sensor can be installed at installation point C between ends A and B of the bridge to collect response data. In this embodiment, ends A and B of the bridge refer to the upper and lower ends of the train, respectively. The sensor can be a displacement sensor or a dynamic strain sensor, which can collect displacement response data and dynamic strain response data at the sensor installation location, respectively.

[0039] The second step is to determine the train position fitting model using a linear fitting method based on the acquisition time and train parameters corresponding to the troughs in the acquired response data. Specifically, the troughs in the response data can be determined by comparing the data magnitudes corresponding to adjacent acquisition time points. For example, when the response data meets... and When this data is identified as a trough, the time of its collection is recorded as _____. In the formula, t represents the data acquisition time, and a is the total number of troughs in the response data.

[0040] According to bridge mechanics analysis, when the response data is at a trough, it indicates that the bridge is in a state of local minimum stress. In actual train operation, the train load changes alternately, and the interval between two adjacent troughs is the length of one train car, denoted as Lchexiang. Simultaneously, combining the bridge structure and train parameters, the distance L1 from the first axle of the train to end A at the first trough can be calculated. For ease of description, the distance from the first axle of the train to end A is used; therefore, the train position at each trough is:

[0041]

[0042] Since the train only spends a few seconds passing the PC track beam, we can assume that the train moves at a constant speed during this phase. Therefore, the linear equations can be constructed as follows:

[0043]

[0044] In the formula, For the train's speed, Let be the time it takes for the first axle of the train to pass end A of the bridge. The speed can be obtained through linear fitting. Hejin Bridge Time .

[0045] Utilize speed Hejin Bridge Time The position x of the first axle of the train at any given time can be obtained, which is the train position fitting model:

[0046] .

[0047] The third step is to construct the vehicle load matrix based on the train position fitting model and solve for the influence lines to obtain the PC track beam influence lines. In this embodiment, the vehicle load matrix can be constructed using interpolation based on the train position fitting model.

[0048] Specifically, using the finite element method, the bridge is divided into multiple nodes. To ensure the accuracy of the influence line, the interval between these nodes is generally no greater than 0.2m. When the nth axle of the train (located as...) When the axis is exactly located at node m of the partition, the entire mass of the axis is applied to that node.

[0049]

[0050] In the formula: n is the nth axle of the train, This represents the weight of the nth axis. This represents the load at the m-th node.

[0051] When the train axle is located between the m-th and (m+1)-th nodes, the weight of the axle is shared by both nodes. A linear weight distribution method is used based on the distance.

[0052]

[0053]

[0054]

[0055] .

[0056] When considering all data collection points and the number of train axles, the vehicle load matrix can be expressed as:

[0057]

[0058] The movement of a train on a track bridge can be viewed as the application of a series of quasi-static concentrated forces on the track bridge; therefore, the bridge response can be expressed as:

[0059]

[0060] In the formula This represents the influence line of the bridge. Generally, the number of rows in the load matrix A is less than the number of columns, so the least constant method can be used to solve for the influence line of the PC track beam.

[0061] A storage medium storing a computer program, characterized in that, when the computer program is executed, it implements the above-described method for determining the influence line of a PC track beam.

[0062] like Figure 2 The system block diagram shown is for the PC track beam influence line measurement system. The measurement system includes:

[0063] The acquisition module is configured to acquire response data of the train passing over the PC track beam;

[0064] The fitting module is configured to determine the train position fitting model by linear fitting based on the acquisition time and train parameters corresponding to the troughs in the response data.

[0065] The solution module is configured to construct the vehicle load matrix based on the train position fitting model and solve for the influence line to obtain the PC track beam influence line.

[0066] Specifically, the measurement system consists of an acquisition module, a fitting module, and a solution module. The acquisition module acquires response data of the train passing over the PC track beam. The acquisition module includes sensors; to acquire the response data, sensors can be installed between ends A and B of the bridge. The response data acquired by the acquisition module is as follows: Figure 3 As shown. In this embodiment, ends A and B of the bridge refer to the train's entry and exit points, respectively. The sensor can be a displacement sensor or a dynamic strain sensor, which can collect displacement response data and dynamic strain response data at the sensor's installation location, respectively.

[0067] The fitting module can determine the train position fitting model using a linear fitting method based on the acquisition time and train parameters corresponding to the troughs in the acquired response data. Specifically, the fitting module can determine the troughs in the response data by comparing the data magnitudes corresponding to adjacent acquisition time points. For example, when the response data meets... and When this data is identified as a trough, the fitting module can record the data acquisition time, denoted as . In the formula, t represents the data acquisition time, and a is the total number of troughs in the response data.

[0068] According to bridge mechanics analysis, when the response data is at a trough, it indicates that the bridge is in a state of local minimum stress. In actual train operation, the train load changes alternately, and the interval between two adjacent troughs is the length of one train car, denoted as Lchexiang. Simultaneously, the fitting module can combine bridge structure and train parameters to calculate the distance L1 from the first axle of the train to end A when the first trough occurs. For ease of description, the distance from the first axle of the train to end A is used; therefore, the train position at each trough is:

[0069]

[0070] Since the train only spends a few seconds passing the PC track beam, we can assume that the train moves at a constant speed during this phase. Therefore, the linear equation constructed by the fitting module can be:

[0071]

[0072] In the formula, For the train's speed, This is the time it takes for the first axle of the train to pass end A of the bridge. The fitting module can obtain the speed through linear fitting. Hejin Bridge Time .

[0073] Utilize speed Hejin Bridge Time The position x of the first axle of the train at any given time can be obtained, which is the train position fitting model:

[0074] .

[0075] The solution module consists of a construction unit and a solution unit. The construction unit can construct the vehicle load matrix based on the train position fitting model. Specifically, the construction unit can use the finite element method to divide the bridge into multiple nodes. To ensure the accuracy of the influence line, the interval between construction units is generally no greater than 0.2m. When the nth axle of the rail train (position denoted as...) When the axis is exactly located at node m of the partition, the entire mass of the axis is applied to that node.

[0076]

[0077] In the formula: n is the nth axle of the train, This represents the weight of the nth axis. This represents the load at the m-th node.

[0078] When the train axle is located between the m-th and (m+1)-th nodes, the weight of the axle is shared by both nodes. A linear weight distribution method is used based on the distance.

[0079]

[0080]

[0081]

[0082] .

[0083] When considering all data collection points and the number of train axles, the vehicle load matrix constructed by the building unit can be expressed as:

[0084]

[0085] The movement of a train on a track bridge can be viewed as the application of a series of quasi-static concentrated forces on the track bridge; therefore, the bridge response can be expressed as:

[0086]

[0087] In the formula This represents the influence line of the bridge. Generally, the number of rows in the load matrix A is less than the number of columns, so the least constant method can be used to solve the element and obtain the influence line of the PC track beam.

[0088] To verify the technical effectiveness of the claimed solution, this embodiment obtains train response data through numerical simulation using a finite element model of a PC track beam. The PC track beam has a span of 20m, and the train load is as follows: Figure 4 As shown, the concentrated load P is 80kN when the train is empty. The train speed is set to 60km / h, and the data acquisition time is advanced by 1 second. The strain response data at mid-span of the PC track beam when the train passes are calculated using self-programmed finite element software, and the results are as follows. Figure 5 As shown.

[0089] Secondly, the vehicle position during the test was determined using trough data; trough time data and parking space position data were obtained by comparing the data sizes of adjacent points and through bridge mechanics analysis. The results are shown in Table 1. Velocity was obtained through linear fitting. and The result is as follows Figure 6 As shown, the velocity is obtained by solving. =16.591m / s (59.728 / h), =0.991s. This is not significantly different from the set speed and initial time, which also reflects the accuracy of this method.

[0090] Utilize speed Hejin Bridge Time The position x of the first axle of the train at any given time can be obtained:

[0091]

[0092] Based on this, the vehicle load matrix and influence lines are constructed, and the equations are solved using the least squares method to obtain the strain influence lines of the PC track beam, as shown below. Figure 7 As shown.

[0093] In addition, to verify the accuracy of the line recognition method, the overall relative error (ORE) and peak relative error (PRE) are defined as follows:

[0094]

[0095]

[0096] in, This indicates the influence of line recognition results. Indicates the baseline influence line; Describing covariance, Indicates variance; This represents the maximum absolute value of all elements in the vector. It can be calculated using the above formula. Figure 7 The overall relative error between the middle influence line identification and the baseline influence line is ORE = 0.08%, and the peak relative error is PRE = 1.31%, indicating that the influence line identification results are relatively accurate.

[0097] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for determining the influence line of a PC track beam, characterized in that, include: Obtain response data of the train passing over the PC track beam; Based on the acquisition time and train parameters corresponding to the troughs in the response data, a train position fitting model is determined through linear fitting, and the linear equation is: ； The train position fitting model is as follows: ； in, For the train's speed, This refers to the time it takes for the first axle of the train to pass the upper end of the bridge. The data collection time is t, which is any time. x is the position of the first axle of the train. The interval between two adjacent trough data points corresponds to the length of one train car, denoted as Lchexiang. L1 is the distance between the first axle of the train and the upper end of the bridge at the first trough. a is the total number of troughs in the response data. Based on the train position fitting model, the vehicle load matrix is ​​constructed to solve for the influence line, thus obtaining the PC track beam influence line. The bridge response can be expressed as: Let A be the influence line of the bridge and A be the load matrix. The influence line is solved using the least squares method to obtain the influence line of the PC track beam. The vehicle load matrix is ​​constructed based on the train position fitting model, including: The bridge is divided into multiple nodes using the finite element method, with intervals no greater than 0.2m. The position of the nth axle of the train... When located at node m of the partition, the entire mass of the axis is applied to that node: n is the nth axle of the train. This represents the weight of the nth axis. This represents the load at the m-th node; When the train axle is between the m-th node and the (m+1)-th node, the weight of the axle is shared by both nodes. The load is distributed between the two nodes linearly according to the distance, and the specific calculation formula is as follows: ； Considering all data collection points and the number of train axles, the vehicle load matrix is ​​represented as: in, Let n represent the load at the m-th node, and n be the n-th axle of the train. This represents the weight of the nth axis.

2. The method for determining the influence line of a PC track beam according to claim 1, characterized in that, The response data includes dynamic displacement response data or dynamic strain response data.

3. A storage medium storing a computer program, characterized in that, When the computer program is executed, it implements the PC track beam influence line determination method as described in claim 1 or 2.

4. A system for determining the influence line of a PC track beam, characterized in that, include: The acquisition module is configured to acquire response data of the train passing over the PC track beam; The fitting module is configured to determine the train position fitting model through linear fitting based on the acquisition time and train parameters corresponding to the troughs in the response data. The linear equation is: ； The train position fitting model is as follows: ； in, For the train's speed, This refers to the time it takes for the first axle of the train to pass the upper end of the bridge. The data collection time is t, which is any time. x is the position of the first axle of the train. The interval between two adjacent trough data points corresponds to the length of one train car, denoted as Lchexiang. L1 is the distance between the first axle of the train and the upper end of the bridge at the first trough. a is the total number of troughs in the response data. The solution module is configured to construct the vehicle load matrix based on the train position fitting model and solve for the influence line to obtain the PC track beam influence line. The bridge response can be expressed as: Let A be the influence line of the bridge and A be the load matrix. The influence line is solved using the least squares method to obtain the influence line of the PC track beam. The vehicle load matrix is ​​constructed based on the train position fitting model, including: The bridge is divided into multiple nodes using the finite element method, with intervals no greater than 0.2m. The position of the nth axle of the train... When located at node m of the partition, the entire mass of the axis is applied to that node: n is the nth axle of the train. This represents the weight of the nth axis. This represents the load at the m-th node; When the train axle is between the m-th node and the (m+1)-th node, the weight of the axle is shared by both nodes. The load is distributed between the two nodes linearly according to the distance, and the specific calculation formula is as follows: ； Considering all data collection points and the number of train axles, the vehicle load matrix is ​​represented as: in, Let n represent the load at the m-th node, and n be the n-th axle of the train. This represents the weight of the nth axis.

5. The PC track beam influence line measurement system according to claim 4, characterized in that, The response data acquired by the acquisition module includes dynamic displacement response data or dynamic strain response data.

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