A calculation method for the impact coefficient of bridges under random vehicle flow based on the screening method

Abstract

The present invention discloses a calculation method for the impact coefficient of a bridge under random vehicle flow based on the screening method, comprising the following steps: S1. Extract the dynamic time history curves of key positions of the bridge under different traffic flow states; S2. Statistically analyze the time history data of the key positions of the bridge according to the dynamic time history curves obtained in S1 to obtain ordered vectors {Y d} and {Y j}. Based on the continuity characteristics of the time history curves at typical positions of the bridge under random vehicle flow, compared with the traditional calculation method for the impact coefficient, the main advantages of the present invention are as follows: It overcomes the limitations of local peaks or valleys in calculating the impact coefficient by the theoretical method under the action of traditional typical vehicles, has a wider application range, and at the same time avoids the inaccuracy of calculating the impact coefficient of the bridge due to the randomness of time period division. It retains the extreme value data of the wave trough sample points of the time history displacement curve to the greatest extent, and significantly improves the accuracy of calculating the impact coefficient of the bridge.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge impact coefficient calculation methods, and particularly relates to a calculation method for the bridge impact coefficient under random vehicle flow based on the screening method. Background Technique

[0002] When a moving vehicle load passes through a bridge, the bridge structure is forced to vibrate under the influence of the vehicle load. In bridge engineering, the load amplification effect caused by this forced vibration is called the impact effect, which is usually described by the bridge impact coefficient. The detection and calculation of the bridge impact coefficient are of extremely profound significance for bridge design and maintenance and reinforcement. If the impact coefficient of the bridge structure cannot be accurately detected, it will lead to unreasonable design of new bridges or untimely maintenance and reinforcement of old bridges, thus easily causing bridge damage caused by vehicle loads, and even major accidents may occur in severe cases.

[0003] At present, the common bridge impact coefficient calculation methods are the theoretical method and the code method. When calculating the bridge impact coefficient using the theoretical method, traffic is usually closed, and typical vehicles (single vehicle or two vehicles side by side passing through the bridge at a certain vehicle speed, the dynamic response at typical positions of the bridge) are used for analysis. As Figure 2 shown, where: the maximum static displacement and the maximum dynamic displacement in the time history curve are y jmax (mm) and y dmax (mm) respectively, and the calculation of the impact coefficient μ is shown in Equation (1):

[0004]

[0005] From the description of the above theoretical method, since the vehicle is single or two vehicles side by side, the determination of the trough value of the dynamic response curve is relatively simple. However, under natural traffic, there are multiple continuous troughs in the dynamic response under actual random vehicle flow, and the corresponding respective trough values cannot be identified by the above theoretical method.

[0006] Code method:

[0007] General Code for Highway Bridges and Culverts in China (JTG D60—2015):

[0008]

[0009] According to Equation (2), it can be seen that the value taken by the code method is an empirical method value, and the calculation of the impact coefficient under random vehicle flow cannot be comprehensively considered.

[0010] Under natural traffic, the time history displacement curve at typical positions of the bridge is as Figure 3 shown. Compared with the relevant actions of typical vehicles, there are multiple trough values in its dynamic time history curve. When calculating using the traditional theoretical method or the code method, the value taken for the impact coefficient is not very reasonable.

[0011] Time - segment division method:

[0012] To solve the problem of unreasonable value - taking of the bridge impact coefficient calculated by the theoretical method, a calculation method of the bridge impact coefficient based on time - segment division is proposed. Its basic principle is as follows: To analyze the dynamic response data of the total operation time - period t (such as 1 day) of the bridge under random vehicle flow, an empirical division of the operation time - period is proposed. For example, the total operation time - period t is divided into n interval time - periods, each interval time - period is Δt, and the maximum dynamic displacement y of the bridge within each Δt interval time - period is analyzed (Δt)d max and the maximum static displacement y (Δt)j max , then a total of n groups of sample data of the dynamic and static displacements of the bridge can be obtained, and the impact coefficient of the bridge is calculated through formula (3).

[0013]

[0014] In the formula:

[0015] μ Δt —The value of the bridge impact coefficient within the Δt interval time - period;

[0016] y (Δt)dmax —The maximum value of the dynamic effect of the control section of the bridge within the Δt interval time - period;

[0017] y (Δt)jmax —The maximum value of the corresponding static effect within the Δt interval time - period.

[0018] However, the value - taking of the bridge impact coefficient under random vehicle flow is greatly affected by the change of the Δt interval, and currently, no reasonable value - taking standard for Δt can be given, and only relevant empirical values can be adopted.

[0019] Whether calculating the bridge impact coefficient by the theoretical method or the code method, or calculating the bridge impact coefficient under random vehicle flow by the time - segment division method, there are certain drawbacks, resulting in a certain deviation between the value - taking of the bridge impact coefficient and the actual situation, and even singularities may occur, with poor accuracy in calculating the bridge impact coefficient, reducing the reliability of using the bridge impact coefficient to judge the bridge state, and unable to play a reference role in the subsequent design or maintenance and reinforcement of the bridge.

[0020] Therefore, in view of the above - mentioned technical problems, it is necessary to provide a calculation method of the bridge impact coefficient under random vehicle flow based on the screening method. Summary of the Invention

[0021] The purpose of the present invention is to provide a calculation method of the bridge impact coefficient under random vehicle flow based on the screening method to solve the problem of poor calculation accuracy of the above - mentioned bridge impact coefficient under random vehicle flow or natural traffic conditions.

[0022] To achieve the above object, the technical solution provided by the embodiment of the present invention is as follows:

[0023] A calculation method for the impact coefficient of a bridge under random vehicle flow based on the screening method, comprising the following steps:

[0024] S1. Extract the dynamic time history curves of the key positions of the bridge under different traffic flow states;

[0025] S2. Statistically analyze the time history data of the key positions of the bridge according to the dynamic time history curves obtained in S1 to obtain the ordered vectors {Y d} and {Y j};

[0026] S3. Adopt the screening principle that if the sample wave trough value at a certain moment is simultaneously less than the sample wave trough values at adjacent moments, then save the data, otherwise eliminate the data, and perform forward and backward difference extraction on the ordered vectors {Y d} and {Y j}, and obtain all the wave trough sample point data sets {Y d1} and the static displacement {Y jimax} by screening the time history data;

[0027] S4. Adopt the screening principle to perform secondary screening on the multiple wave trough sample point data sets {Y d1} obtained in S3. The secondary screening is used to screen and eliminate the wave trough sample points that are not the maximum values in the wave trough sample point data set {Y d1}, and obtain the secondary screening retained time displacement wave trough sample data {Y d2};

[0028] S5. Adopt the screening principle to perform tertiary screening on the secondary screening retained time displacement wave trough sample data {Y d2}, obtain the tertiary screening retained time displacement wave trough sample data {Y d3}, and judge whether there are sample data greater than 0 in the tertiary screening retained time displacement wave trough sample data {Y d3}. If there are sample data greater than 0, perform re-screening on the tertiary screening retained time displacement wave trough sample data {Y d3} until the extreme values of the screened sample wave troughs are all less than 0, so as to screen and eliminate the wave trough sample points with wave trough values greater than 0 in the secondary screening retained time displacement wave trough sample data {Y d2};

[0029] S6. Perform the K-S test on the finally retained bridge response extreme value data, and obtain the 95% confidence interval as the representative values Y drmax and Y jrmax of the dynamic and static displacement wave troughs.

[0030] Further, the time history curve of the key positions of the bridge in S1 is calculated and analyzed by using a self-developed random vehicle-bridge coupling vibration analysis program. Calculating and analyzing the time history curve of the key positions of the bridge by using the random vehicle-bridge coupling vibration analysis program is convenient for improving the accuracy of the extracted time history curve.

[0031] Further, for the measured time history data of the key positions of the bridge in S1, the test data needs to be denoised and filtered during the statistical analysis process, which is convenient for obtaining the real data of the bridge dynamic response and improves the accuracy of calculating the impact coefficient of the bridge.

[0032] Further, the time history data of the key positions of the bridge in S2 is statistically analyzed by using Matlab software. Statistically analyzing the key positions of the bridge by using Matlab software improves the convenience and accuracy of statistically analyzing the dynamic displacement vector and static displacement vector of the bridge.

[0033] Further, in S2, the ordered vectors {Y d} and {Y j} are arranged in chronological order, and the corresponding time series vector {T} is saved. Arranging {Y d} and {Y j} in chronological order provides convenience for subsequent screening of the ordered vectors {Y d} and {Y j}. At the same time, through the correspondence between the time series vector {T} and the ordered vectors {Y d} and {Y j}, the accuracy of screening the orderly connected {Y d} and {Y j} is improved.

[0034] Further, the impact coefficient calculation formula in S7 is where μ r is the representative value of the bridge impact coefficient.

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] Based on the continuity characteristics of the time - history curve at typical positions of the bridge under random vehicle flow, which has the characteristics of multiple peaks and valleys, compared with the traditional calculation method of impact coefficient, its main advantages are as follows: it overcomes the limitations of local peaks or valleys in calculating the impact coefficient by the theoretical method under the action of traditional typical vehicles, has a wider application range, and at the same time avoids the inaccuracy of calculating the bridge impact coefficient due to the randomness of time - period division. It retains the extreme value data of the wave - valley sample points of the time - history displacement curve to the greatest extent, significantly improves the accuracy of calculating the bridge impact coefficient, greatly improves the reliability of judging the bridge state through the bridge impact coefficient, has a wider application range, can be used for the calculation and analysis of the bridge impact coefficient under natural traffic conditions without closing the traffic, has higher calculation efficiency and calculation accuracy, and can play an accurate reference role in the subsequent design or repair and reinforcement of bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0038] Figure 1 It is a flow chart of a method for calculating the bridge impact coefficient under random vehicle flow based on the screening method in the embodiment of the present invention;

[0039] Figure 2 It is a calculation diagram of the theoretical bridge impact coefficient in the embodiment of the present invention;

[0040] Figure 3 It is a calculation diagram of the bridge impact coefficient based on time - period division in the embodiment of the present invention;

[0041] Figure 4 It is the time - history response curve of the dynamic displacement of the typical cross - section in the embodiment of the present invention;

[0042] Figure 5 It is the dynamic displacement response curve of the time - period interval in the embodiment of the present invention;

[0043] Figure 6 It is a schematic diagram of time - period interception in the embodiment of the present invention;

[0044] Figure 7 It is a schematic diagram of screening local interference wave valleys in the embodiment of the present invention;

[0045] Figure 8 It is a scatter diagram of the wave - valley scatter points of the displacement curve after the first screening of a method for calculating the bridge impact coefficient under random vehicle flow based on the screening method in the embodiment of the present invention;

[0046] Figure 9 It is the valley broken line graph of the first screening displacement curve of a calculation method for the bridge impact coefficient under random vehicle flow based on the screening method in the embodiment of the present invention;

[0047] Figure 10 It is the valley scatter plot of the second screening displacement curve of a calculation method for the bridge impact coefficient under random vehicle flow based on the screening method in the embodiment of the present invention;

[0048] Figure 11 It is the valley broken line graph of the second screening displacement curve of a calculation method for the bridge impact coefficient under random vehicle flow based on the screening method in the embodiment of the present invention;

[0049] Figure 12 It is the valley scatter plot of the third screening displacement curve of a calculation method for the bridge impact coefficient under random vehicle flow based on the screening method in the embodiment of the present invention;

[0050] Figure 13 It is the valley broken line graph of the third screening displacement curve of a calculation method for the bridge impact coefficient under random vehicle flow based on the screening method in the embodiment of the present invention;

[0051] Figure 14 It is the statistical chart of the third screening result of a calculation method for the bridge impact coefficient under random vehicle flow based on the screening method in the embodiment of the present invention;

[0052] Figure 15 It is the full-time displacement curve of the original curve and the third screening in the embodiment of the present invention;

[0053] Figure 16 It is the local-time displacement curve of the original curve and the third screening in the embodiment of the present invention. Specific embodiments

[0054] The present invention will be described in detail below in conjunction with the embodiments shown in the drawings. However, these embodiments do not limit the present invention, and any structural, methodical, or functional transformation made by those of ordinary skill in the art based on these embodiments is included in the protection scope of the present invention.

[0055] The present invention discloses a calculation method for the bridge impact coefficient under random vehicle flow based on the screening method. Referring to Figure 1 as shown, it includes the following steps:

[0056] S1. Extract the dynamic time history curves of the key positions of the bridge under different traffic flow states;

[0057] S2. Statistically analyze the time history data of the key positions of the bridge according to the dynamic time history curves obtained in S1 to obtain the ordered vectors {Y d} and {Y j}};

[0058] S3. Adopt the screening principle that if the sample trough value at a certain moment is simultaneously less than the sample trough values at adjacent moments, then save the data; otherwise, eliminate the data, and perform forward and backward difference value extraction on the ordered vectors {Y d}} and {Y j}}. Obtain all the trough sample point data sets {Y d1}} and the static displacement {Y jimax}} by screening the time history data;

[0059] S4. Adopt the screening principle to perform secondary screening on the multiple trough sample point data sets {Y d1}} obtained in S3. The secondary screening is used to screen and eliminate the trough sample points that are not the maximum values in the trough sample point data sets {Y d1}}, and obtain the secondary screening retained time displacement trough sample data {Y d2}};

[0060] S5. Adopt the screening principle to perform tertiary screening on the secondary screening retained time displacement trough sample data {Y d2}}, obtain the tertiary screening retained time displacement trough sample data {Y d3}}, and judge whether there are sample data greater than 0 in the tertiary screening retained time displacement trough sample data {Y d3}}. If there are sample data greater than 0, perform re-screening on the tertiary screening retained time displacement trough sample data {Y d3}} until the extreme values of the screened sample troughs are all less than 0, which is used to screen and eliminate the trough sample points with trough values greater than 0 in the secondary screening retained time displacement trough sample data {Y d2}};

[0061] S6. Perform K-S test on the finally retained bridge response extreme value data, and obtain the 95% confidence interval as the representative values Y drmax and Y jrmax of the dynamic and static displacement troughs;

[0062] S7. Calculate the representative value μ r of the bridge impact coefficient according to the impact coefficient formula.

[0063] Reference Figure 1 As shown, the time history curve at the key position of the bridge in S1 is calculated and analyzed by using a random traffic flow vehicle-bridge coupling vibration analysis program. Calculating and analyzing the time history curve at the key position of the bridge by using a random traffic flow vehicle-bridge coupling vibration analysis program is convenient for improving the accuracy of the extracted time history curve.

[0064] At the same time, when the random traffic-bridge coupling vibration analysis program is used to calculate and analyze the bridge, there is no need to close traffic on both sides of the bridge, which avoids traffic jams caused by closing the bridge and improves the convenience of calculating and analyzing the bridge.

[0065] Specifically, in the statistical process of the time history data of the key positions of the bridge in S1, the test data needs to be denoised and filtered to facilitate the acquisition of real data of the dynamic response of the bridge and improve the accuracy of the calculation of the impact coefficient of the bridge.

[0066] Preferably, the time-history data of the key positions of the bridge in S2 are statistically analyzed using Matlab software. By using Matlab software to perform statistical analysis on the key positions of the bridge, the convenience and accuracy of statistical analysis of the dynamic displacement vector and static displacement vector of the bridge are improved.

[0067] refer to Figures 4 - 5 As shown, the ordered vector {Y d} and {Y j} are arranged in chronological order, and the corresponding time series vector {T} is saved. By d} and {Y j} are arranged in chronological order as the subsequent ordered vector {Y d} and {Y j} provides convenience for screening, and at the same time, the time series vector {T} and the ordered vector {Y d} and {Y j}, which improves the correspondence between the ordered connected {Y d} and {Y j}Accuracy of screening.

[0068] Ginseng Figures 4 - 7 As shown, the screening principle in S3 is that if the sample trough value at a certain moment is simultaneously smaller than the sample trough value at the adjacent moment, the data is saved, otherwise the data is discarded. By adopting the screening principle to screen the sample trough value, the extreme value data of the trough sample point of the time-history displacement curve can be retained to the greatest extent.

[0069] Specifically, the screening principle is to d} and {Y j} to take the front and back differences, that is, t i The time history response value at the time and the adjacent time on both sides (t i-1 ) and (t i+1 ) displacement value is compared, if t i The displacement value Y at the moment di Greater than (t i-1 ) and (t i+1 ) The displacement value Y at the momentd(i-1) and Y d(i+1) ,Y d(i-1) ≤Y di ≥Y d(i+1) ,Y di As the reserved trough value after screening and record its moment t i .

[0070] If this principle is not satisfied, then eliminate this data and judge the next moment t i+1 Response value, and thus cycle through all time history response data for one screening to obtain all trough sample point data sets {Y d1} and static displacement {Y jimax} of the bridge.

[0071] Reference Figure 4 As shown, there are multiple troughs in the displacement time history response of the mid-span mid-section of the bridge. Affected by the operation duration, its displacement response curve is relatively dense. To illustrate the relevant principles of the screening method proposed in this paper, relevant data within the time period Δt ∈ [57, 67] are intercepted for analysis.

[0072] Refer Figure 5 As shown, within the time period of Δt ∈ [57, 67], there are a total of 10 trough points, namely A1 to A10. Among them, the trough points of A2 and A9 are the trough extremes expected to be screened out in this paper, while A1, A3 to A8, and A10 represent interference trough values and need to be eliminated during the screening process.

[0073] When using the screening principle to screen A1, A3 to A8, and A10, the screening process is as follows:

[0074] Step1: A1 > A2 < A3, the condition is satisfied, retain A2;

[0075] Step2: A2 < A3 < A4, the condition is not satisfied, eliminate A3;

[0076] Step3: A3 < A4 < A5, the condition is not satisfied, eliminate A4;

[0077] Step4: A4 < A5 < A6, the condition is not satisfied, eliminate A5;

[0078] Step5: A5 < A6 < A7, the condition is not satisfied, eliminate A6;

[0079] Step6: A6 < A7 < A8, the condition is not satisfied, eliminate A7;

[0080] Step7: A7 > A8 < A9, the condition is not satisfied, retain A8;

[0081] Step 8: A8 > A9 < A10, the condition is satisfied, and A9 is retained;

[0082] Through step 1 to step 8, the expected wave trough extreme values A2 and A9 can be obtained.

[0083] Reference Figure 6 As shown, when determining the wave trough values A1 to A10, it is found that there are local interfering wave trough values around each wave trough value. To illustrate such problems, based on Figure 5 , taking the wave trough value of A6 as an example, relevant data in a relatively small time section of Δt ∈ [63.4 - 64.0] is intercepted for analysis;

[0084] Reference Figures 6 - 7 As shown, it can be known that when Δt ∈ [63.4, 64.0], there are a total of five wave trough values of A6, B1 to B4 on the bridge dynamic displacement curve within a time interval of less than 1 s. Among them, A6 is the maximum wave trough point of the curve and is the expected wave trough point, and B1 to B4 are interfering wave trough points. Such situations exist in the entire time history curve. Therefore, it is necessary to use the relevant principles of the above screening method to eliminate the interfering wave trough points of B1 to B4

[0085] Specifically, the calculation formula for the impact coefficient in S7 is In the formula, μ r is the representative value of the bridge impact coefficient.

[0086] Among them, when under Class B pavement and in the case of the vehicle flow condition of level two acting on the bridge;

[0087] Reference Figures 8 - 9 As shown, after one screening, the total number of wave trough points is 516, and the number of wave trough points corresponds one-to-one with the time series.

[0088] Reference Figures 10 - 11 As shown, after two screenings, the total number of wave trough points is 134, and the number of wave trough points corresponds one-to-one with the time series.

[0089] Reference Figures 12 - 13 As shown, after three screenings, the total number of wave trough points is 44, and all the retained displacement values are negative. The sample data after three screenings is used for the K - S test.

[0090] Reference Figure 14 As shown, the dynamic and static displacement sample data both pass the K - S test. Among them, Y dmax =-11.08 mm, Y jrmax =-7.81 mm, then the impact coefficient μ = 0.419.

[0091] Reference Figures 15 - 16As shown, the envelope curve of the sample after three - stage screening is quite consistent with the original wave - trough maximum curve, and the wave - trough extreme - value data randomly intercepted in the time period Δt ∈ [205, 225] also meet the expected extreme values for screening, verifying the correctness of the method.

[0092] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above - mentioned exemplary embodiments, and without departing from the original intention or basic characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, from any point of view, the embodiments should be regarded as exemplary and non - restrictive. The scope of the present invention is defined by the appended claims rather than the above description. Thus, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be embraced within the present invention. Any reference signs in the claims should not be construed as limiting the claims involved.

[0093] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other implementation manners understandable to those skilled in the art.

Claims

1. A calculation method for the impact coefficient of a bridge under random traffic flow based on the screening method, characterized in that, it includes the following steps: S1. Extract the dynamic time history curves of the key positions of the bridge under different traffic flow states; S2. Statistically analyze the time history data at the key positions of the bridge according to the power time history curve obtained in S1 to obtain ordered vectors {Y d} and {Y j}; S3. Apply the screening principle that if the sample trough value at a certain moment is simultaneously less than the sample trough values at adjacent moments, then save the data; otherwise, eliminate the data to perform forward and backward difference calculations on the ordered vectors {Y d} and {Y j}, and obtain all the trough sample point data sets {Y d1} and the static displacement {Y jimax} by screening the time history data; S4. Apply the screening principle to perform secondary screening on the multiple valley sample point datasets {Y obtained in S3 d1}. The secondary screening is used to screen out and remove the valley sample points that are not the maximum values in the valley sample point dataset {Y d1}, and obtain the secondary screening retained time displacement valley sample data {Y d2}; S5. Use the screening principle to perform three - stage screening on the sample data of the trough of the secondary screening retention time displacement {Y d2}, obtain the sample data of the trough of the three - stage screening retention time displacement {Y d3}, and judge whether there is sample data greater than 0 in the sample data of the trough of the three - stage screening retention time displacement {Y d3}. If there is sample data greater than 0, perform re - screening on the sample data of the trough of the three - stage screening retention time displacement {Y d3} until the extreme values of the sample troughs after screening are all less than 0, which is used to screen and eliminate the trough sample points with trough values greater than 0 in the sample data of the trough of the secondary screening retention time displacement {Y d2}; S6. Perform the K-S test on the extreme values of the finally retained bridge response data, and obtain the 95% confidence interval as the representative values Y of the dynamic and static displacement troughs drmax and Y jrmax ; S7. Calculate the representative value μ of the bridge impact coefficient according to the impact coefficient formula r .

2. The calculation method for the impact coefficient of a bridge under random traffic flow based on the screening method according to claim 1, characterized in that, in S1, the time history curves of the key positions of the bridge are calculated and analyzed by using a self-developed random traffic flow vehicle-bridge coupling vibration analysis program.

3. The calculation method for the impact coefficient of a bridge under random traffic flow based on the screening method according to claim 1, characterized in that, for the measured time history data of the key positions of the bridge in S1, noise reduction and filtering processing need to be performed on the test data before the statistical analysis process.

4. The calculation method for the impact coefficient of a bridge under random traffic flow based on the screening method according to claim 1, characterized in that, in S2, the time history data of the key positions of the bridge are statistically analyzed by using Matlab software.

5. The calculation method for the impact coefficient of a bridge under random traffic flow based on the screening method according to claim 1, characterized in that, In the above S2, the ordered vectors {Y d} and {Y j} are arranged in chronological order, and the corresponding time series vector {T} is saved simultaneously.

6. The calculation method for the impact coefficient of a bridge under random traffic flow based on the screening method according to claim 1, characterized in that, The impact coefficient calculation formula in S7 is where μ r is the representative value of the bridge impact coefficient.

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