A rapid detection method for weak side end of bridge support based on vehicle vibration signal

Abstract

A rapid detection method for the weak side end of a bridge support based on a vehicle vibration signal. The detection technology involved in the present invention is an "indirect measurement method". It only requires the sensor to be placed on the vehicle (measuring vehicle) passing the bridge, and there is no need to place the sensor on the bridge. It can greatly improve the detection efficiency and will not interfere with normal traffic. The present invention proposes a method for detecting the weak side end of a bridge support based on the vibration signal of a vehicle passing the bridge. It can quickly and accurately screen out bridges with inconsistent left and right supports, identify the weak side end of the bridge support, and provide a reference for the fixed-point refined manual inspection of the bridge support. The detection method of the present invention can eliminate the influence of road surface unevenness, can eliminate the interference of the vehicle's own vibration, and is sensitive to the weak support end of the bridge.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge maintenance and management, and in particular relates to an indirect rapid detection method for the weak side end of a bridge support using the response of a vehicle passing over the bridge. Background Art

[0002] Supporting components such as piers and bearings are the basic elements of the boundary constraints of bridge structures and are closely related to the safety and stability of bridges. Due to the influence of material aging, traffic loads, especially overloads, bridge supporting components often fail, resulting in the loss of stiffness on one or both sides of the bridge support. The detection of bridge supporting components is an important part of the safety inspection of bridge structures.

[0003] At present, the engineering inspection of bridge supports is still mainly based on visual inspection. However, since the supporting structure is located under the main body of the bridge, inspection engineers often need to use auxiliary equipment such as bridge inspection vehicles or elevators, which has low inspection efficiency and the inspection results are greatly affected by subjective factors.

[0004] In recent years, some scholars have initially explored bridge support inspection methods based on drones and climbing robots, which can avoid engineers' high-altitude operations and save manpower, but the inspection is still mainly based on taking photos, and can only detect surface cracks and other damage, and the inspection efficiency has not been significantly improved. On the other hand, due to the small size of bridge bearings and their concealment between the bridge end and the pier, drones and climbing robots are generally unable to detect bridge bearings. Summary of the invention

[0005] The technical problem to be solved by the present invention is how to construct a response index for detecting the weak side end of a bridge support, while eliminating the influence of the vehicle's own interference and the road surface flatness to improve the detection sensitivity.

[0006] To achieve the above purpose, the technical solution adopted by the present invention is:

[0007] A rapid detection method for the weak side end of a bridge support based on a vehicle vibration signal is characterized by constructing a "forward and reverse signal envelope ratio" index that can sense the inconsistent conditions of the left and right supports of the bridge, that is, formula (8). When the "forward and reverse signal envelope ratio" index is applied, it can eliminate the adverse effects of the vehicle's own interference and the adverse effects caused by the flatness of the road surface, thereby improving the detection sensitivity.

[0008] A method for quickly detecting the weak side end of a bridge support based on a vehicle vibration signal, which specifically includes the following steps when applied:

[0009] (1) Arrange the acceleration sensor on the vehicle: Install the acceleration sensor on the front and rear axles A1 and A2 of the dual-axle vehicle;

[0010] (2) Acceleration data collection: A dual-axle vehicle drives across the bridge to be tested in both the forward and reverse directions at a constant speed. The signal acquisition system records two sets of data obtained by the sensor: the front and rear axle data collected in the forward direction are recorded as and The data of the front and rear axles collected during reverse driving are recorded as and

[0011] (3) Obtaining velocity and displacement data: For the two sets of acceleration data obtained in step (2), and and Integrate time t to get the speed response and and By integrating again, we can obtain the displacement responses y1(t) and y2(t), and

[0012] (4) Extracting the envelope of the forward and reverse signals: Using the Hilbert function and formula (7), the envelope of the forward and reverse vehicle vibration signals are extracted, which are denoted as E and E respectively. + and E - :

[0013]

[0014] (5) Calculate the envelope ratio of the forward and reverse signals: Use formula (8) to calculate the envelope ratio of the forward and reverse signals, and determine the weak side of the bridge support based on the ε value. ε>1 indicates that the vibration signal amplification occurs on the left side of the bridge where the vehicle departs in the forward direction. This is called the "weak side amplification" phenomenon, and this end is determined to be the weak side of the support. On the contrary, ε<1 indicates that the right side of the bridge is the weak side of the support.

[0015]

[0016] Beneficial Effects

[0017] The detection method of the present invention can eliminate the influence of road surface unevenness, can eliminate the interference of vehicle body vibration itself, and is sensitive to the weak supporting end of the bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The vehicle-bridge coupling model used for theoretical verification of the present invention

[0019] Figure 2 The dual-axle inspection vehicle travels in reverse on the elastic support beam

[0020] Figure 3 The vehicle body of a double-axle vehicle passing through the elastic support beam in both forward and reverse directions and the signal difference envelope of the front and rear axles of the vehicle body of the present invention DETAILED DESCRIPTION

[0021] The purpose of the present invention is to disclose a detection method, provide theoretical derivation and example verification; the algorithm of the present invention has application value and prepares for the subsequent development of a special detection vehicle.

[0022] A rapid detection method for the weak side end of a bridge support based on a vehicle vibration signal is characterized by constructing the dynamic balance equations (1) and (2) that can characterize the front and rear axles of a dual-axle vehicle, thereby mathematically deducing the forward and reverse signal envelope ratio of equation (8) that can sense the inconsistent conditions of the left and right supports of the bridge. When the forward and reverse signal envelope ratio indicator is used, it has the effect of eliminating the adverse effects of the vehicle's own interference and the adverse effects caused by the flatness of the road surface, thereby improving the detection sensitivity.

[0023] The equations (1) and (2) are: Assume that the vertical acceleration response of the front and rear axles is and Its dynamic balance equation can be expressed as:

[0024]

[0025]

[0026] Where y1(t) and y2(t) represent the vertical displacements of points A1 and A2 directly above the front and rear axles. and is the corresponding acceleration; d is the distance between the front and rear axles, d1 and d2 are the distances between the front and rear axles and the center of gravity C of the vehicle body, m v and J v represents the vehicle mass and moment of inertia, k1 and k2 represent the front and rear axle suspension stiffness; u1(t) and u2(t) represent the bridge contact point displacement response at the front and rear wheels at time t, respectively; r(x)| x＝vt and r(xd)| x＝vt Respectively represents the flatness of the bridge pavement at the front and rear wheels.

[0027] The formula (7) is used to calculate the front and rear axle signal difference envelopes of the vehicle in the forward and reverse directions, respectively, which are denoted as E + and E -

[0028]

[0029] The formula (8) is used to calculate the forward and reverse signal envelope ratio

[0030]

[0031] A method for quickly detecting the weak side end of a bridge support based on a vehicle vibration signal, which specifically includes the following steps when applied:

[0032] (1) Arrange the acceleration sensor on the vehicle: Install the acceleration sensor on the front and rear axles A1 and A2 of the dual-axle vehicle;

[0033] (2) Acceleration data collection: A dual-axle vehicle drives across the bridge to be tested in both the forward and reverse directions at a constant speed. The signal acquisition system records two sets of data obtained by the sensor: the front and rear axle data collected in the forward direction are recorded as and The data of the front and rear axles collected during reverse driving are recorded as and

[0034] (3) Obtaining velocity and displacement data: For the two sets of acceleration data obtained in step (2), and and Integrate time t to get the speed response and and By integrating again, we can obtain the displacement responses y1(t) and y2(t), and

[0035] (4) Extracting the envelope of the forward and reverse signals: Using the Hilbert function and formula (7), the envelope of the forward and reverse vehicle vibration signals are extracted, which are denoted as E and E respectively. + and E - :

[0036]

[0037] (5) Calculate the envelope ratio of the forward and reverse signals: Use formula (8) to calculate the envelope ratio of the forward and reverse signals, and determine the weak side of the bridge support based on the ε value. ε>1 indicates that the vibration signal amplification occurs on the left side of the bridge where the vehicle departs in the forward direction. This is called the "weak side amplification" phenomenon, and this end is determined to be the weak side of the support. On the contrary, ε<1 indicates that the right side of the bridge is the weak side of the support.

[0038]

[0039] Mechanism description and beneficial effects of the technical solution of the present invention

[0040] In actual engineering, bridge support damage is often manifested as a loss of support stiffness on one or both sides, with one side being weaker than the other.

[0041] The working mechanism of the present invention is as follows: the reduction of support stiffness caused by damage to the bridge support will change the constraints of the bridge structure, causing the bridge structure to no longer be a mechanically symmetrical structure, and the behavior of the bridge dynamic system caused by the forward and reverse driving of the vehicle will be inconsistent. Due to the vehicle-bridge coupling mechanism, the forward and reverse driving vibration signals of the vehicle will also be inconsistent, and have an obvious "weak side amplification" phenomenon, that is, the vibration response of the vehicle-bridge system caused by the vehicle starting from the weak side end of the bridge is greater than the response starting from the other side. Furthermore, the "forward and reverse signal envelope ratio" index proposed in the present invention can be calculated through the vehicle vibration signal. This index can effectively eliminate the influence of the two main interference factors of road surface unevenness and vehicle's own vibration at the same time, and can significantly enhance the vehicle's perception sensitivity to the weak side end of the bridge support.

[0042] The method proposed by the invention has the advantages of being rapid, economical, easy to operate, and highly maneuverable.

[0043] The detection technology involved in the present invention is an "indirect measurement method", which only requires the sensor to be placed on the vehicle passing the bridge (measuring vehicle), without the need to place the sensor on the bridge. It can greatly improve the detection efficiency and will not interfere with normal traffic.

[0044] The present invention proposes a method for detecting the weak side end of a bridge support based on the vibration signal of a vehicle passing over the bridge. The method can quickly and accurately screen out bridges with inconsistent left and right supports, identify the weak side end of the bridge support, and provide a reference basis for the fixed-point refined manual inspection of bridge supports.

[0045] The effect verification of the technical solution of the present invention (theoretical verification)

[0046] The "forward and reverse signal envelope ratio" index mentioned in the present invention has three main characteristics:

[0047] (1) Eliminate the influence of road surface roughness;

[0048] (2) Eliminate the vibration interference of the vehicle body itself;

[0049] (3) Sensitive to the weakly supported end of the bridge.

[0050] The following will be verified one by one:

[0051] Step 1: Confirm that the “forward and reverse signal envelope ratio” can eliminate the influence of road surface roughness.

[0052] In actual measurement, the acceleration sensor is more convenient to install on the front and rear axles of the vehicle. Assume that the vertical acceleration response of the front and rear axles is and Its dynamic balance equation can be expressed as:

[0053]

[0054]

[0055] Where y1(t) and y2(t) represent the vertical displacements of points A1 and A2 directly above the front and rear axles. and is the corresponding acceleration; d is the distance between the front and rear axles, d1 and d2 are the distances between the front and rear axles and the center of gravity C of the vehicle body, m v and J v represents the vehicle mass and moment of inertia, k1 and k2 represent the front and rear axle suspension stiffness; u1(t) and u2(t) represent the bridge contact point displacement response at the front and rear wheels at time t, respectively; r(x)| x＝vt and r(xd)| x＝vt Respectively represent the bridge road surface roughness at the front and rear wheels. Obviously, the road surface roughness r(x)| x＝vt and r(xd)| x＝vt It is included in the vehicle kinematic equations (1) and (2), mixed into the vehicle motion, and interferes with the vehicle's perception sensitivity to the bridge beam and support.

[0056] However, it can be found that the bridge pavement smoothness r(x)| x＝vt and r(xd)| x＝vt There is a temporal and spatial correlation, that is, the road surface roughness experienced by the wheels at the same time t always differs by a distance d in the spatial domain; if the rear wheel is virtually moved forward by a time interval d / v in the time domain, the road surface roughness experienced by the rear wheel can be expressed as r(x)| x＝v(t+d / v) In other words, there is always a time difference d / v when the front and rear wheels pass the same position (road surface flatness) on the bridge.

[0057] Perform the following mathematical transformation on the formula: formula (1) × d2 + formula (2), formula (1) × d1 - formula (2), we can get:

[0058]

[0059]

[0060] Here, the left side of the equation is the external excitation input of the front and rear axles, respectively, the vertical deflection displacements u1(t) and u2(t) of the bridge at the front and rear wheel positions under the action of the vehicle load, and the road surface roughness r(x)| experienced by the front and rear wheels. x＝vt and r(xd)| x＝vt The right side of the equation is the combined response related to the vehicle body vibration signal, which are all known quantities.

[0061] Shift the left and right sides of equation (3) by the time interval d / v, and then subtract equation (4) to obtain the displacement response difference between the front and rear axles:

[0062]

[0063] Derivative the above formula twice with respect to time t, we can get the acceleration response difference between the front and rear axles, which can be expressed as

[0064]

[0065] Obviously, through the above mathematical transformation, the acceleration response difference between the front and rear axles has eliminated the road surface roughness r(x)| x＝vt and r(xd)| x＝vt impact.

[0066] Performing Hilbert transform on equation (6) yields the envelope of the vehicle vibration signal:

[0067]

[0068] Obviously, the signal envelope does not include the road roughness. Further calculation of the envelope ratio of the positive and reverse signals:

[0069]

[0070] Because E + Both E- and E- do not contain information about road surface roughness, so the "positive and negative signal envelope ratio" indicator ε proposed in the present invention can eliminate the influence of road surface roughness.

[0071] Step 2: Confirm that the "forward and reverse signal envelope ratio" indicator eliminates the interference of the vehicle's own vibration.

[0072] The present invention adopts Figure 1 The vehicle-bridge coupling mechanical model shown reveals the analytical expression of the "forward and reverse signal envelope ratio" indicator. The bridge is represented by an Euler-Bernoulli beam, and the left and right supports of the bridge are assumed to be two linear springs with unequal stiffness, and the stiffness is recorded as k l and k r The kinematic equation of the elastic support beam under the action of the moving vehicle body is expressed as:

[0073]

[0074] In the formula represents the mass per unit length of the beam, E represents the elastic modulus, I represents the section inertia moment, and u represents the displacement of the beam. F(x,t) represents the force acting on the bridge by the vehicle body, which is expressed as

[0075]

[0076] Where v represents the vehicle speed, δ(·) is the Dirac function, and H(·) is the unit step function. j =(j-1)d / v, where subscripts 1 and 2 represent the front and rear axles of the vehicle, respectively. Since the vehicle mass is much smaller than the bridge mass The force exerted by the vehicle body on the bridge is mainly its own gravity load, and the vehicle-bridge dynamic coupling effect has little effect. At this time, the front and rear axle forces are approximately equal to the vehicle body gravity, that is, p j =-m v g / 2, where g represents the acceleration due to gravity.

[0077] In order to obtain the analytical expression, the mode superposition method is used to solve the beam response. It is assumed that the beam displacement response u(x, t) is approximately expressed as a combination of multiple beam vibration modes φ n (x) and the response modal response q n (t) composition, i.e.

[0078]

[0079] The vibration mode expression of the elastically supported beam is:

[0080]

[0081] Where λ n is the frequency parameter, γ and β are dimensionless auxiliary parameters:

[0082]

[0083]

[0084]

[0085] Where α = k r / k l , which represents the ratio of the right support stiffness to the left support stiffness of the bridge.

[0086] Substitute equation (12) into equation (9), and multiply both sides by the vibration mode function φ n (x), integrate along the beam length L, and then use the orthogonality condition and initial condition to obtain the bridge modal response q n The expression of (t) is:

[0087]

[0088] In the formula, Δ stn is the static displacement of the bridge under vehicle gravity load, ω n is the bridge modal frequency, Ω n (=λ n v / L) is the driving frequency, S nis the speed parameter, and the expressions are:

[0089]

[0090] In the formula,

[0091] The displacement response of the bridge (contact point) at the contact point positions P1 and P2 between the front and rear axles and the bridge can be expressed as:

[0092] u1(t)=∑ n q n (t)φ n (x)| x＝vt (16a)

[0093] u2(t)=∑ n q n (t)φ n (xd)| x＝vt (16b)

[0094] It can be seen from the above formula that at time t, the front and rear wheels of the vehicle act on different positions of the bridge, which are x and xd respectively. Mathematically, we can move the bridge displacement response u2(t) corresponding to the rear axle forward by the time interval d / v to obtain u2(t+d / v), and then subtract the bridge displacement response u1(t) corresponding to the front axle, and finally obtain the displacement signal difference between the front and rear axles, that is,

[0095] u resi (t) = u2(t+d / v)-u1(t) = ∑ n [q n (t+d / v)-q n (t)]φ n (vt) (17)

[0096] The above formula can be further expanded as:

[0097]

[0098] In the formula, a n 、b n 、c n d n and e n Represents the amplitude coefficient of each main frequency, and Represents the phase angle of each main frequency. The specific expanded expressions of these physical quantities are shown in Appendix A.

[0099] By taking the derivative of equation (18) twice, we can get the expression of the front and rear axle acceleration signal difference, namely:

[0100]

[0101] By performing Hilbert transformation on equation (19), we can obtain the envelope of the acceleration signal difference between the front and rear axles:

[0102]

[0103] From the above formula, we can find that: the envelope data E of the vehicle's forward and reverse vibration signals + and E - Only the bridge frequency term ω is included in n , driving frequency term Ω n (=λ n v / L), and the bridge frequency shows left and right bifurcation, that is, ω n -Ω n and ω n +Ω n , which can be used as the identification feature of the bridge frequency. On the other hand, the driving frequency term Ω n is often much smaller than the bridge frequency term, which does not affect the bridge frequency identification. More important discovery: E + and E - The frequency of the vehicle body vibration itself is not included in the equation, which means that the interference of the vehicle body itself has been eliminated.

[0104] Furthermore, the "forward and reverse signal envelope ratio" index ε obtained based on equations (8) and (20) also does not include the vehicle body's own vibration frequency term, which means that the index proposed in the present invention can eliminate the influence of the vehicle body's own interference.

[0105] Step 3: Confirm that the “forward and reverse signal envelope ratio” is sensitive to the weak support end of the bridge

[0106] When the stiffness of the left and right supports of the bridge is inconsistent, the bridge will evolve into an "asymmetric" structure, and the vibration signal of the vehicle on the bridge will change with the driving direction. The above has given the analytical expression of the vibration response of the vehicle driving forward from the left end of the bridge. The following will show the dynamic behavior of the vehicle driving in the reverse direction from the right end of the bridge.

[0107] To facilitate mechanical expression, the coordinate system is mirrored around the mid-span of the bridge, see Figure 2 At this time, the beam motion equation and modal vibration mode expressions are the same as the vehicle forward driving expressions, and the modal response q n The expression of the acceleration response difference between the front and rear axles (t) is the same as that of the forward driving. The difference is that the left support stiffness k in equation (13) is l The right side support stiffness k is required r Replacement, and the support stiffness ratio α needs to be Replace. At this time, the physical parameter expression corresponding to the vehicle driving in the opposite direction from the right side of the bridge is:

[0108]

[0109]

[0110] The parameter k r =αk l and Substituting into equation (13a), it can be found that equation (21a) is actually exactly the same as equation (13a), which shows that the frequency parameter λ n It is an inherent property of the bridge and is not affected by the direction of vehicle travel.

[0111] However, due to k r Not equal to k l , the auxiliary parameter in formula (21b) will also not be equal to the auxiliary parameter γ in equation (13b). Specifically, the auxiliary parameter corresponding to the vehicle's reverse driving is The stiffness k of the right supporting end of the bridge r The auxiliary parameter γ corresponding to the vehicle's forward travel is inversely proportional to the left support stiffness k of the bridge. l From formula (20) and Appendix A, it can be found that the amplitude coefficients a of the signal difference between the front and rear axles of the vehicle body are n ,b n ,c n ,d n , and e n Approximation and auxiliary parameters γ or It is directly proportional to the acceleration signal of the front and rear axles. and its envelope E + and the left side support stiffness k l Inversely proportional; when the vehicle is driving in the opposite direction from the right, the front and rear axle acceleration response difference and its envelope E - and the right side support stiffness k of the bridge r Assume that when the support stiffness on the right side of the bridge weakens, k r <k l The vibration signal envelope caused by the reverse running of the detection vehicle from the right end is bound to be E - Greater than the signal envelope E generated by driving forward from the left + , that is, the "weak side amplification" phenomenon.

[0112] According to the definition of envelope ratio in formula (8), when the support stiffness on the right side of the bridge weakens, that is, k l >k r , at this time ε<1; on the contrary, if the support stiffness on the left side of the bridge weakens k l <k r, at this time ε>1. On the contrary, we can infer which side of the bridge support has weakened according to the "forward and reverse signal envelope ratio" index proposed in this invention.

[0113] Summary: Through the above three steps, it is theoretically confirmed that the "positive and negative signal envelope ratio" indicator can identify the weak side ends of the left and right supports of the bridge, and this indicator can effectively eliminate the interference of road roughness and vehicle vibration, ensuring the recognition sensitivity of the weak side end of the bridge.

[0114] The effectiveness of the method proposed in the present invention will be verified by finite element numerical simulation as follows.

[0115] The vehicle and bridge parameters are shown in Table 1. The bridge bearing parameters are the parameters corresponding to the rubber bearing model GBZY200×42 (CR) in the national standard JT / T4-2019, and the stiffness is 3.29×10 8 N / m. Assuming that the support stiffness of the left support remains unchanged, the support stiffness of the right support is reduced to k r =0.658×10 8 The first four modal frequencies of the bridge can be calculated by equation (13b), which are 1.80, 6.78, 13.59 and 21.58 Hz, respectively, and the vehicle's own frequency is 3.73 Hz.

[0116] Table 1 Vehicle-bridge system parameters used in numerical simulation

[0117]

[0118] In order to simulate the actual measurement environment more realistically, the following influencing parameters will be considered in the numerical simulation. The bridge pavement roughness is based on the international standard ISO 8608, and the B-level pavement roughness spectrum is selected to generate the pavement roughness spatial information. The beam damping is assumed to be Rayleigh damping, and the damping ratio is 3%. The bridge support damping is 18MN·s / m according to the specification recommendation. The measurement and noise errors are uniformly considered as environmental noise, and the noise level is E p =5%.

[0119] Figure 3 The vibration signal of the vehicle body (front axle) of a dual-axle vehicle passing through the elastic support beam in both forward and reverse directions and the signal difference envelope of the front and rear axles of the vehicle body of the present invention are shown. Figure 3 (a) The vehicle body vibration time domain signal shows that when the test vehicle starts from the weak side (right end) of the bridge and drives in the reverse direction, the vibration signal recorded is slightly larger than the signal when the vehicle starts from the left side of the bridge and drives in the forward direction. However, the difference between the forward and reverse bidirectional signals is very small, making it difficult to clearly identify the "weak side amplification" phenomenon. Figure 3 (b) It can be found from the vehicle vibration frequency domain signal that due to the uneven road surface, the vehicle's own vibration is significantly amplified, and its frequency f vThe peak value is significantly higher than the bridge frequency peak value, which seriously affects the indirect detection effect of the bridge.

[0120] The vehicle vibration signal is converted into the front and rear axle signal difference envelope E through formula (7): + and E - ,like Figure 3 (c) It can be clearly observed that the signal envelope E corresponding to the detection vehicle starting from the weak side of the bridge and driving in the opposite direction - Significantly greater than the forward driving index E + , the phenomenon of "weak side amplification" is extremely significant. + and E - Substituting the data into equation (8), we can obtain the envelope ratio of the forward and reverse signals ε = 0.12 < 1, which clearly indicates that the right side support of the bridge is the weak side end.

[0121] Going further, compare Figure 3 From the spectra of (d) and 3(b), we can find that the signal difference between the front and rear axles of the vehicle used to calculate the forward and reverse signal envelope ratio has completely excluded the vibration frequency of the vehicle body itself, so the first four frequencies of the bridge can be clearly identified, and the peak frequency of the bridge traveling in the reverse direction from the weak side is significantly greater than that of the other side. So far, we can determine that the starting bridge end of the reverse driving of the detection vehicle is the weak side end of the bridge support stiffness through the "weak side amplification" of the "forward and reverse signal envelope ratio" index proposed by the present invention.

[0122] Appendix A: Expressions for the amplitude coefficients and phase angle expansion of each main frequency in equation (18)

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

Claims

1. A method for rapid detection of weak side ends of bridge supports based on vehicle vibration signals, characterized in that: Construct the "forward and reverse signal envelope ratio" index that can sense the inconsistency between the left and right supports of the bridge, that is, formula (8); The application includes the following steps: (1) Arrange the acceleration sensor on the vehicle: Install the acceleration sensor on the front and rear axles A1 and A2 of the two-axle vehicle; (2) Acceleration data collection: A dual-axle vehicle drives across the bridge to be tested in both the forward and reverse directions at a constant speed. The signal acquisition system records two sets of data obtained by the sensor: the data collected from the front and rear axles in the forward direction are recorded as , the front and rear axle data collected during reverse driving are recorded as ; (3) Obtaining velocity and displacement data: For the two sets of acceleration data obtained in step (2), and , Separately for time Integrate to get the speed response and , and , and integrate again to obtain the displacement response and , and ; (4) Extracting the envelope of the forward and reverse signals: The Hilbert function is used to extract the envelope of the forward and reverse vehicle vibration signals using equation (7), which are respectively expressed as and : In the formula, and It represents the vertical displacement of points A1 and A2 directly above the front and rear axles. is the corresponding acceleration; d is the distance between the front and rear axles, and are the distances between the front and rear axles and the center of gravity C of the vehicle body, represents the vehicle mass and moment of inertia, and Indicates the suspension stiffness of the front and rear axles; t represents time; In the formula, Indicates the vehicle speed, is the Diktonic function, is a unit step function; , where subscripts 1 and 2 represent the front and rear axles of the vehicle body respectively; the vehicle body mass ; (5) Calculate the envelope ratio of the forward and reverse signals: Use formula (8) to calculate the envelope ratio of the forward and reverse signals. The value determines the weak side end of the bridge support; This indicates that the vibration signal amplification occurs on the left side of the bridge where the vehicle is heading in the forward direction. This is called the "weak side amplification" phenomenon. This end is determined to be the weak side end of the support. This indicates that the right side of the bridge is the weak side end of the support; 。

Images