Damage identification method of beam bridge based on statistical moment curvature coupled vibration

Abstract

The present invention belongs to the technical field of building structure damage identification, and specifically relates to a method for identifying damage of a beam bridge based on statistical moment curvature of vehicle-bridge coupled vibration. Step 1: using a mobile test vehicle to obtain acceleration signals at corresponding measuring points of the bridge; Step 2: processing the collected acceleration signals and calculating the fourth-order statistical moment of the acceleration response; Step 3: calculating the statistical moment curvature through the obtained acceleration statistical moment of each measuring point, and drawing a difference curve to identify the damage position; Step 4: obtaining the unit stiffness of the bridge through the obtained statistical moment curvature by a model correction method, so as to identify the damage degree of the bridge. The present invention can still perform good bridge damage identification under the influence of various factors (unit damage degree, bridge damping ratio, environmental noise); the statistical moment curvature index has higher noise resistance and efficiency than the flexibility curvature and mode curvature indexes. At the same time, by comparing the existing bridge damage transmission rate theoretical identification method, it is found that for single and multiple bridge damages, the index proposed by the present invention has a better effect on damage location and damage degree judgment, and the identification error is smaller.

Description

Technical Field

[0001] The invention belongs to the technical field of building structure damage identification, and in particular relates to a statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration. Background Art

[0002] Structural health monitoring mainly refers to the strategies and processes for damage identification and characterization of engineering structures. Structural damage can be identified through characteristic indicators that can reflect the changes in structural material parameters and geometric characteristics, and the damage of the current structure can be determined through statistical analysis of characteristic indicators. The current damage identification methods can be divided into frequency domain indicator type and time domain indicator type according to characteristic indicators.

[0003] For the study of frequency domain indicators, Zhao Yunpeng et al. used the modal flexibility curvature difference to locate the damage of special-shaped bridges without noise influence; Xiang Changsheng et al. identified the damage position of bridges by using the modal curvature index based on information entropy; He Wenyu et al. used the modal curvature difference index combined with the vehicle-bridge coupling dynamics principle to identify bridge damage; Pandey et al. obtained the displacement mode shapes of two models through finite element analysis, and used the central difference approximation to calculate the modal curvature shape from the displacement mode shape to judge the damage; Feng et al. proposed a method for bridge damage detection, numerically simulated the calculation of the first-order modal vibration mode curvature of the bridge by directly extracting the bridge displacement response, and then carried out damage identification research; the above existing technologies generally have the disadvantages of poor noise resistance and low recognition efficiency. Zhang et al. then proposed a new damage characteristic index MOSS (Mode Shape Square), which analyzed the difference in MOSS curves before and after the bridge damage, and then judged whether the bridge was damaged; this index has a certain noise resistance ability, and the damage identification effect is better at a lower speed, but the influence of road roughness is not considered, and the recognition efficiency is low. Xiang Zhihai proposed a damage detection method for striking a mobile test vehicle. This method uses the MAC (Modal assurance criterion) damage judgment index defined by the acceleration spectrum to locate the bridge damage position. However, the method of damage identification only through frequency-related judgment indicators has inherent defects. Oshima et al. used a heavy truck to amplify the vibration response of the bridge, simulated the signals of multiple single-axis test vehicles to identify the modal vibration shape of the bridge, and thus identified the bridge damage; Yang Yang et al. believed that bridge damage is often reflected in the reduction of bridge stiffness, so a new method was used to identify the bridge unit stiffness through the relationship between vibration shape and stiffness. Studies have shown that this method can effectively identify bridge damage, but it is more dependent on the accuracy of the extracted modal vibration shape; the robustness of the method to noise needs to be further improved.

[0004] For the study of time domain indicators, the existing technology obtains the structural damage information matrix through the random subspace method, and then establishes the damage characteristic index. This method can better identify the degree of damage, but the method is inefficient and not suitable for signals with large changes. The existing technology uses the residual of the time series model as an indicator to identify structural damage by fusing Kalman filtering and generalized autoregressive conditional heteroscedasticity. This method can better identify structural damage, but the method requires massive data support. The existing technology forms a new method for structural damage identification based on the time series model by establishing an autoregressive model with external input. This method has a certain recognition effect, but it is heavily dependent on the measured data after fitting. Zhang et al. proposed to apply statistical moments to structural damage identification, but only studied the optimization application of statistical moment indicators in simple plane shear frame structures. The existing technology proposed to use statistical moments to identify single curved simply supported beams, but the recognition results of statistical moment indicators for curved structures are not ideal.

[0005] Through the above analysis of existing technologies, it can be seen that both time domain and frequency domain indicators based on damage identification have problems such as poor noise resistance and low recognition efficiency, and the damage identification method based on traditional curvature indicators, which is more sensitive to the damage location, is more obvious. Traditional bridge damage identification requires a large number of sensors to be placed on the bridge to be tested on site for testing, which brings many inconveniences to traffic and consumes huge manpower and material resources. Summary of the invention

[0006] In view of the above-mentioned deficiencies existing in the prior art, the present invention provides a statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration to solve the above-mentioned problems existing in the prior art identification methods.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] The damage identification method of the statistical moment curvature beam bridge based on vehicle-bridge coupled vibration includes the following steps:

[0009] Step 1: Use a mobile test vehicle to obtain acceleration signals at corresponding measuring points on the bridge;

[0010] Step 2: Process the collected acceleration signal and calculate the fourth-order statistical moment of the acceleration response;

[0011] Step 3: Calculate the statistical moment curvature through the acceleration statistical moment of each measuring point, and draw the difference curve to identify the damage location; Step 4: Use the obtained statistical moment curvature through the model correction method to obtain the unit stiffness of the bridge, so as to identify the damage degree of the bridge.

[0012] Furthermore, the method of obtaining the acceleration signal in step 1 is specifically as follows:

[0013] The motion equations of the mobile excitation vehicle and the bridge are:

[0014]

[0015]

[0016] Where: q v are the vertical acceleration and displacement of the mobile excitation vehicle respectively; u b is the vertical displacement of the bridge; for To find the partial derivative with respect to time; u b ""for is the partial derivative of displacement; δ, x and t are Diktral function, horizontal displacement and action time; The uniform quality of the bridge.

[0017] Using the modal superposition method, the motion equation of the stationary test vehicle can be further obtained using equations (1) and (2):

[0018]

[0019]

[0020] Furthermore, the step 2 of calculating the acceleration statistical moment is specifically as follows:

[0021] When the mean value of the acceleration signal is zero, the second-order acceleration statistical moment can be expressed as:

[0022]

[0023] Further, the step three is specifically as follows:

[0024] The statistical moment index M4 can be expressed as:

[0025] M4=[M4(x1),M4(x2),.......,M4(x N )] (19)

[0026] Then, the central difference method is used to obtain the statistical moment curvature curve of the statistical moment curve. The statistical moment curvature values ​​of each measuring point of the bridge in the previous state are compared. The curvature values ​​of the measuring points in different states are subtracted by formula (26) to draw the statistical moment curvature difference curve along the longitudinal direction of the bridge. The bridge damage position can be obtained based on the measuring points with prominent changes in the curve. Formula (26) is:

[0027]

[0028] Further, the step 4 is specifically as follows:

[0029] An objective function with statistical moment curvature as a parameter is constructed to realize bridge model correction and obtain the damage degree of the bridge.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] (1) The bridge damage identification method based on statistical moment curvature can still perform bridge damage identification well under the influence of various factors (unit damage degree, bridge damping ratio, and environmental noise);

[0032] (2) Compared with the flexibility curvature and mode curvature indices, the statistical moment curvature index has higher noise resistance and efficiency. By comparing the existing theoretical identification methods of bridge damage transmissibility, it is found that the index proposed in the present invention has a better effect on damage location and damage degree judgment for single and multiple bridge damages, and the identification error is smaller.

[0033] (3) Compared with the traditional modal curvature index, the method of the present invention avoids the relatively cumbersome operation of obtaining modal parameters and the problem of incomplete information, and has the advantage of higher recognition efficiency;

[0034] (4) The method of the present invention theoretically establishes for the first time the relationship between the statistical moment curvature and the vibration mode and stiffness in the multi-degree-of-freedom of a bridge. Then, combined with the vehicle-bridge coupled vibration theory, the applicability of the method under different environmental noise, damage degree and bridge damping factors is explored. At the same time, the method is compared with other traditional curvature indicators for the damage location and traditional transmissibility identification methods for the damage degree. Finally, the method is verified through real bridge tests, providing effective support for the practical application of the method of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A simplified model diagram of vehicle-bridge coupled vibration according to an embodiment of a statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration according to the present invention;

[0036] Figure 2 It is a flow chart of bridge damage identification according to an embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0037] Figure 3 A schematic diagram of the Minxie Bridge in accordance with an embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0038] Figure 4 It is a schematic diagram of numerical simulation division units of an embodiment of a statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0039] Figure 5 The four units of the embodiment of the damage identification method for beam bridge based on the statistical moment curvature of vehicle-bridge coupled vibration of the present invention are different ζ under the damage condition.n The statistical moment curvature difference curve diagram below;

[0040] Figure 6 The statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration according to the present invention is shown in Figure 2 for different ζ values ​​under 4-unit and 7-unit damage conditions. n The statistical moment curvature difference curve diagram below;

[0041] Figure 7 It is a statistical moment curvature difference curve diagram of four units at different damage degrees in an embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0042] Figure 8 It is a statistical moment curvature difference curve diagram of different damage degrees of 4 and 7 units in the embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0043] Fig. 9 The four units of the embodiment of the damage identification method of the beam bridge based on the statistical moment curvature of the vehicle-bridge coupled vibration of the present invention are different S under the damage condition. NR The statistical moment curvature difference curve diagram below;

[0044] Fig.10 The statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention is shown in Figure 4 and 7 under different S NR The statistical moment curvature difference curve diagram below;

[0045] Fig.11 It is a curvature difference curve diagram under different curvature indices under 7-unit damage conditions of an embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0046] Fig.12 This is a comparison result diagram of the damage degree of unit stiffness identified by two methods under 4 unit damage conditions in an embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0047] Fig.13 This is a comparison result diagram of the damage degree of unit stiffness identified by two methods under 4-unit and 7-unit damage conditions in an embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0048] Fig.14 This is a graph of acceleration signals collected at 6 nodes by a test vehicle ① of an embodiment of a statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0049] Fig.15This is a graph of acceleration signals collected at 7 nodes by a test vehicle ② of an embodiment of a statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0050] Fig.16 ① A spectrum diagram of the acceleration signal of the vehicle body of the test vehicle of the embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0051] Fig.17 It is a spectrum diagram of the acceleration signal of the vehicle body of the test vehicle ② of the embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0052] Fig.18 This is a diagram showing the arrangement of measuring points in the first span of the Minxie Bridge according to an embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention (unit: m);

[0053] Fig.19 This is a diagram showing the statistical moment curvature identification result of the first span of the Minxie Bridge in an embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention;

[0054] Fig. 20 This is a diagram of statistical moment curvature identification results of the first span of the Minxie Bridge in an embodiment of the statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration of the present invention. DETAILED DESCRIPTION

[0055] In order to enable those skilled in the art to better understand the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0056] 1 Theoretical basis

[0057] 1.1 Vehicle-bridge coupled vibration theory

[0058] Matching with the actual bridge test, Figure 1 The simplified dynamic model of the vehicle-bridge continuous beam. All model parameters in the figure are shown in Table 1. The continuous beam is simplified to a uniform and equal-section Euler Bernoulli beam. L and EI represent the bridge length and cross-sectional bending stiffness, respectively. The vehicle-bridge coupled vibration studied in this invention is to simulate the random traffic flow to generate external excitation by a single-degree-of-freedom mobile excitation vehicle. Two single-degree-of-freedom vehicles are used as test vehicles, which are stationary on the bridge to collect the response signal of the bridge. Based on the above method, a structural dynamic motion model is established, and the following assumptions are made: 1) Since the test method is to collect the static state of the test vehicle with a sensor, the dynamic model does not need to consider the roughness of the bridge surface; 2) Since the mass of the test vehicle and the mobile excitation vehicle is much smaller than the mass of the bridge, the vehicle mass can be ignored; 3) In order to simplify the dynamic model, the theoretical derivation does not consider the damping ratio of the mobile excitation vehicle and the bridge, but subsequent research will analyze the damping ratio of the bridge as an influencing factor; 4) It is assumed that the motion state of the mobile excitation vehicle is uniform.

[0059] Table 1 Parameter definitions of different types of vehicles

[0060]

[0061] Note: The mass blocks ◎, ① and ② connected by springs represent the mobile excitation vehicle and the two stationary test vehicles respectively.

[0062] The motion equations of the mobile excitation vehicle and the bridge are:

[0063]

[0064]

[0065] Where: q v are the vertical acceleration and displacement of the mobile excitation vehicle respectively; u b is the vertical displacement of the bridge; for To find the partial derivative with respect to time; u b ""for is the partial derivative of displacement; δ, x and t are Diktral function, horizontal displacement and action time; The uniform quality of the bridge.

[0066] Among them, the interaction force between the mobile excitation vehicle and the bridge is c (t) can be expressed as:

[0067] f c (t) = -m v g+k v (q v (t)-u b (x,t)| x＝vt ) (3)

[0068] Where g is the acceleration due to gravity.

[0069] The existing technology uses the modal superposition method to obtain the acceleration response solution of the moving excitation vehicle. And the acceleration response solution of the bridge deck contact point It is also proved that in the ideal case without vehicle body damping and bridge deck roughness, the acceleration response of the tire-bridge contact point can better extract the bridge modal parameters, but in the case of actual bridge deck roughness, it is difficult to calculate the corresponding contact point response using the moving vehicle body response. Therefore, the present invention places sensors on two test vehicles and collects the vehicle body acceleration response signals when the vehicle is stopped, and then inverts the contact point response. This method is not affected by the bridge deck roughness. The control equation of the stationary test vehicle can be expressed as:

[0070]

[0071]

[0072] Where: q v , are the vertical displacement, velocity and acceleration of the test vehicles ① and ② respectively. The contact point response of the test vehicle can be calculated using equations (4) and (5).

[0073] 1.2 Analysis of multi-degree-of-freedom statistical moment theory

[0074] It is known from the prior art that the displacement response signals of the axle contact points of the mobile excitation vehicle and the stationary test vehicle can be used to establish the following relationship through Fourier transform:

[0075] W b (x,w)=H bv W v (w) (6)

[0076] In the above formula: W b (x,w) is the frequency domain response relationship of the vertical displacement of the contact point between the bridge and the test vehicle, W v (w) is the vertical displacement frequency domain response relationship of the mobile excitation vehicle. bv is the transfer function of the contact point response between the bridge and the test vehicle, and its expression is:

[0077]

[0078] Where w is the frequency of the mobile excitation vehicle; φ j (d) is the vibration mode value of the j-th continuous beam at x=d; H j (w) is the j-th order frequency response function of the continuous beam; Ω j is the generalized quality value of the bridge at the jth frequency, and the relationship is:

[0079]

[0080] From the knowledge of structural dynamics, we know that the power spectrum density function of the displacement response of the bridge contact point and the frequency domain response of its vertical displacement have the following relationship:

[0081]

[0082] Where S b (w) represents the power spectral density function of the displacement response of the bridge contact point; T represents the length of signal truncation. Within the linear elastic range, the relationship between the response signal variance and the statistical moment is:

[0083]

[0084] In the formula, and M2(v1d1) It is the variance and second-order statistical moment of the vertical displacement response of the vehicle-bridge contact point of the test vehicle ① when the continuous beam x=d1.

[0085] Formulas (7), (8) and (9) are solved together with Formula (10), and according to the orthogonality of the mode vibration shape, the formula is integrated over x from 0 to L, and we have:

[0086]

[0087] Among them, w v It represents the frequency of the moving excitation vehicle. Similarly, when x=d2, the second-order statistical moment M of the displacement of the test vehicle ① 2(v2d2) .

[0088] From the approximate results of narrow-band response, it can be seen that when the damping is low, the variance of the acceleration response and the displacement response has the relationship of formula (12). From the relationship of formula (12), formula (13) can be obtained:

[0089]

[0090] Among them, and They represent the acceleration response variance and the second-order center distance of the vehicle-bridge contact point at the bridge (referred to as the second-order moment of acceleration), ω n Represents the order frequency of the structure.

[0091]

[0092] In formula (13), M 2(v1d1) and M 2(v2d2) They represent the second-order statistical moments of the displacement of the vehicle-bridge contact point response at x = d1 and x = d2, respectively, where M 2(a1d1) and M 2(a2d2) They represent the second-order statistical moments of acceleration of the vehicle-bridge contact point response at x=d1 and x=d2 of the bridge respectively.

[0093] Substitute equation (11) into equation (13), and let M 2(a1d1) M 2(a2d2) have to:

[0094]

[0095] When the mean value of the acceleration signal is zero, the second-order acceleration statistical moment can be expressed as:

[0096]

[0097] γ j (t i ) represents the jth vibration mode under t iThe regular coordinates corresponding to the time structure; N represents the number of sampling points of the measurement point; t i represents the time corresponding to the i-th sampling point. Thus, the first-order fundamental frequency signal of the bridge structure is extracted, and equation (15) is rewritten as:

[0098]

[0099] in, It represents the second-order statistical moment of acceleration of the vehicle-bridge contact point of the test vehicle ① at the bridge in response to the first-order fundamental frequency signal, which is related to the excitation of the excitation vehicle. Similarly, the second-order moment of acceleration of the vehicle-bridge contact point of the test vehicle ② at the bridge in response to the first-order fundamental frequency signal can be obtained.

[0100] Using the same situation as equation (14), for two measurement points that collect signals simultaneously, when the external excitation remains consistent. Compare have:

[0101]

[0102] According to formula (23), the constant parameter is introduced It can be expressed by simplifying the formula:

[0103]

[0104] According to the prior art, for N measuring points evenly distributed on the structure, the interval is h, and the fourth-order statistical moment index M4 of acceleration is re-expressed as:

[0105] M4=[M4(x1),M4(x2),.......,M4(x N )] (19)

[0106] In the formula, x i ~x N is the coordinate of the measuring point, and the difference between adjacent coordinates is h. The first-order central difference of the fourth-order statistical moment of acceleration at the i-th point is M4'(x i )for:

[0107]

[0108] The second-order central difference M4" (x i )for:

[0109]

[0110] The statistical moment curvature index can be obtained by combining the above formulas:

[0111]

[0112] From formula (18), we can get:

[0113]

[0114] in, It represents the second-order statistical moment of the acceleration of the first-order fundamental frequency signal of the structure at position i, v ij Represents the vibration mode value at the jth frequency position i of the structure.

[0115]

[0116] Combining equations (30), (26) and (31), we can obtain:

[0117]

[0118] In the formula is the statistical moment curvature of the structure at position i, v ij represents the displacement at position i, k represents the stiffness, and h 2 and is a constant. It can be seen from the formula that the statistical moment curvature is a display formula related to the vibration mode, and with the change of the vibration mode, it can be converted into a function of stiffness. The change of structural damage is directly related to stiffness. At the same time, the existing technology proves that the difference of curvature indicators can produce better results for damage identification. Therefore, the absolute difference of the statistical moment curvature is:

[0119]

[0120] in, and They represent the statistical moment curvature of the j-th vibration mode measuring point i of the first-order fundamental frequency signal of the damaged structure and the undamaged structure respectively.

[0121] In order to further identify the damage degree of the bridge, the objective function is constructed based on the statistical moment curvature and the bridge model is corrected at the same time, so as to obtain the damage condition of the bridge. Due to space limitations, the detailed stiffness correction process can refer to the existing technology.

[0122] 1.3 Bridge structure damage identification process

[0123] The damage identification method adopted by the present invention is a two-step method: the first step is to process the collected signal and identify the damage location through the obtained statistical moment curvature difference curve; the second step is to obtain the unit stiffness of the bridge through the obtained statistical moment curvature through the model correction method, so as to identify the damage degree of the bridge. The specific process is as follows:

[0124] First, under the towing of the tractor, the acceleration response signals of adjacent designated measuring points are synchronously collected by using two test vehicles at rest, and the statistical moment curvature of the corresponding signals is calculated by using equations (4), (5) and (22). This operation is repeated until the signal collection and statistical moment curvature value calculation of all measuring points of the entire span of the bridge are completed.

[0125] Then, the statistical moment curvature values ​​of each measuring point of the bridge in the previous state are compared, and the curvature values ​​of the measuring points in different states are subtracted by formula (26) to draw the statistical moment curvature difference curve along the longitudinal direction of the bridge. The damage position of the bridge can be obtained based on the measuring points with prominent changes in the curve.

[0126] Finally, an objective function with statistical moment curvature as a parameter is further constructed to realize bridge model correction and obtain the damage degree of the bridge.

[0127] The method flow chart is as follows Figure 2 As shown:

[0128] 2 Numerical simulation

[0129] 2.1 Bridge parameter settings

[0130] The Minxie Bridge on the expressway section of Fuling District, Chongqing City was used as the numerical simulation model, and the relevant parameters were set according to the first span of the bridge. Figure 3 As shown in the figure, the first span of the bridge is 20m long and the concrete grade is C50, which is E = 3.45×10 10 N / m 2 , I=1.23m 4 .

[0131] The distance between the two test vehicles of the present invention is set to 2m, and the bridge test span is divided into 10 units. Figure 4 This is a simplified diagram of the division of bridge units. It can be seen from the figure that each rectangular block represents a unit of the bridge and is represented by the form of "unit + number". For example, the third unit is represented by "unit ③". Numbers 0 to 10 are the numbers at the unit nodes, that is, the location numbers where the test vehicle is parked.

[0132] According to the actual bridge test and vehicle parameter settings, the masses of the two test vehicles are m v1 =m v2 =1470kg, the damping value of the test vehicle is c v1 =c v2 =1000N·s·m -1 , the stiffness value of the test vehicle is k v1 =k v2 =524076N·m -1 , the test vehicle body frequency is w v1 =w v2 =3Hz, the damping value and stiffness value of the mobile excitation vehicle are consistent with the parameters of the traditional conventional vehicle, which are c v0 =2500N·s·m -1 and k v0 =399000N·m -1Random traffic flow Considering four mobile excitation vehicles with different vehicle speeds, different masses and different bridge entry times, the random excitation is approximately simulated, as shown in Table 2. The four mobile excitation vehicles continuously circulate on the bridge according to the contents of Table 2 until the stationary test vehicle completes signal collection.

[0133] Table 2 Changes in external incentives

[0134]

[0135] The data collection method and steps of the two stationary test vehicles can refer to the existing technology. After the node data collection is completed, follow Figure 2 The process constructs the statistical moment curvature difference curve of the bridge unit node, so as to identify the damage location of the bridge unit.

[0136] Since the method of the present invention uses the back-calculated contact point signal and the bridge vibration signal obtained after filtering, the influence on the bridge response signal is relatively small when using different test vehicle masses and damping values, as well as random traffic excitation, and the prior art also shows that different test vehicle masses, damping and random traffic excitation have relatively small influence on bridge damage identification, which can be ignored. Therefore, the present invention selects the bridge damping ratio, bridge damage degree and environmental noise as the analysis influencing parameters of the proposed method.

[0137] 2.2 Study on damage location identification under different bridge damping ratios

[0138] The parameters of the test vehicle and the excitation vehicle used are the same as those in Section 2.1. Under the damage condition of 20% damage degree of the fourth unit of the bridge and the damage condition of 20% damage degree of the fourth and seventh units, the bridge damping ratios of 0.00 (no damping), 0.01, 0.02, 0.03 and 0.04 are studied and plotted. Figure 5 and Figure 6 Normalized acceleration fourth-order statistical moment curvature difference curve.

[0139] from Figure 5 and Figure 6 It can be seen that under different bridge damping ratios, the single damage condition has a sudden change peak at node 4, and the double damage condition has a sudden change peak at nodes 4 and 6. At the same time, the normalized acceleration fourth-order statistical moment curvature difference curves obtained under different damping ratios under the same damage condition basically overlap, indicating that the change in the bridge damping ratio basically does not affect the statistical moment curvature difference. Therefore, under different damping ratios, the method of the present invention can accurately determine the damage location. In order to be closer to the actual engineering bridge damping value, the damping ratio of the present invention is selected as 0.03 in subsequent research.

[0140] 2.3 The influence of different degrees of bridge damage on the identification effect of the proposed method

[0141] The parameters of the test vehicle and the excitation vehicle used are the same as those in Section 2.1. The bridge damping ratio is ζ n =0.03; five groups of different damage conditions of 20%, 25%, 30%, 35%, and 40% were set for bridge 4 units and 4 and 7 units, and the Figure 7 and Figure 8 Normalized acceleration fourth-order statistical moment curvature difference curve.

[0142] Depend on Figure 7 and Figure 8 It can be found that under the influence of different unit damage degrees, the single damage condition has a mutation peak at node 4, and the double damage condition has mutation peaks at nodes 4 and 6, indicating that the statistical moment curvature index can increase with the increase of the unit damage degree, and can better identify unit damage.

[0143] 2.4 Research on damage location identification under different environmental noises

[0144] In the actual data collection environment, the influence of environmental noise on the signal is inevitable. In order to further explore the anti-noise ability of the statistical moment curvature damage identification method based on statistical moment theory, white noise is added to the signal collected by the test vehicle to simulate the polluted signal. The signal-to-noise ratio is used as the judgment of the added noise intensity in reference to the prior art. The greater the noise intensity, the higher the signal-to-noise ratio S. NR The smaller it is.

[0145] The parameters of the test vehicle and the excitation vehicle used are the same as those in Section 2.1. The bridge damping ratio is ζ n = 0.03, select two working conditions: the damage degree of bridge 4 units is set to 20% and the damage degree of 4 units and 7 units are set to 20%, respectively, and set no noise and S NR =20,30,40dB, a total of 4 groups of different noise levels, through Figure 2 The recognition process of the normalized acceleration fourth-order statistical moment curvature difference curve is drawn, such as Fig. 9 and Fig.10 shown.

[0146] Depend on Fig. 9 and Fig.10 It can be found that under the influence of different signal-to-noise ratios (especially the case of 20dB), whether it is a single working condition with 20% damage set at 4 nodes or a multi-damage working condition with 20% set at 4 nodes and 7 nodes respectively, the structural damage position can be significantly obtained by analyzing the measurement points with prominent changes in the curve. The analysis results show that the damage identification method proposed by the present invention can solve the influence of environmental noise on the identification results to a certain extent.

[0147] 2.5 Comparative analysis of recognition effects of different curvature indicators

[0148] In order to further compare the identification effect of the statistical moment curvature index proposed in this invention with the traditional mode curvature index and flexibility curvature index on the location of structural damage, the relevant parameters of the test vehicle and the excitation vehicle in Section 2.1 are firstly adopted, and the bridge damping ratio is ζ n =0.03, 7 units are set to 20% damage degree; then the bridge signal is obtained by the vehicle-bridge coupled vibration theory, the obtained signal is noised by 20dB, and then the statistical moment curvature difference curve, the mode curvature difference curve obtained by the prior art, and the flexibility curvature difference curve obtained by the prior art are respectively obtained by the method of the present invention, and the damage positions are respectively identified and compared, such as Fig.11 shown.

[0149] Fig.11 It is the curvature difference curve under different curvature indexes of 7 units. It can be seen from the figure that although the modal curvature, flexibility curvature and statistical moment curvature indexes have mutations in 7 units, the modal curvature and flexibility curvature indexes are misjudged to a great extent in other positions, and the damage position of the structure cannot be identified by the index curve, while the statistical moment curvature index curve has obvious characteristics and can well identify the damage position of the structure, indicating that the statistical moment curvature index is better than the modal curvature and flexibility curvature in the case of large noise, has higher noise resistance and higher efficiency, and is more conducive to the identification of bridge damage positions in actual situations.

[0150] 2.6 Comparative analysis of methods for identifying unit damage degree based on statistical moment curvature and traditional transmissibility theory

[0151] In order to improve the applicability of the method, the statistical moment curvature index is used to obtain the unit stiffness of the bridge through the model correction method, so as to further identify the damage degree of the bridge; and compared with the bridge damage identification method based on the transmissibility theory proposed in the prior art.

[0152] The parameters of the test vehicle and the excitation vehicle used are the same as those in Section 2.1. The bridge damping ratio is ζ n =0.03, adding signal-to-noise ratio S NR =20dB noise, set single damage and multiple damage conditions, 4 units set 20% damage condition; 4 and 7 units set 20% damage condition, and then use the above two methods to identify unit stiffness damage respectively.

[0153] Fig.12 and Fig.13 The following are comparison diagrams of the damage degree identification effect of the unit stiffness using statistical moment curvature and transmissibility theory under different damage conditions. Fig.12 and 13The comparison results of the unit stiffness identification show that the error of the unit stiffness identification method proposed in the present invention is within 1% under both damage conditions, while the error of the unit stiffness identification method based on the transmissibility theory is relatively large. Under the single damage condition, the error of the lossy unit stiffness identification is 7.5%, and the error of the lossless unit stiffness identification is 12%. Under the multi-damage condition, the error of the lossy unit stiffness identification is 5.7%, and the error of the lossless unit stiffness identification is 15%. It can be seen that the recognition effect of the method proposed in the present invention is better, especially in the case of complex environmental noise. As shown in Table 3, the advantage of this method is obvious.

[0154] Table 3 Time efficiency of different methods for damage identification

[0155]

[0156] 3 Real bridge test

[0157] In order to further verify the reliability of this method in actual engineering applications, a real bridge test was used. The bridge selected was the Minxie Bridge on the Mawu Class I Highway section in Fuling District, Chongqing. The bridge is a three-span continuous beam bridge, each span is 20m, and the first span was selected as the test span. According to the on-site design data, the full width of the bridge deck is 20m, mainly composed of two 9.25m driving lanes and three 0.5m guardrails, and the beam height is 1.5m; the concrete strength grade is C50, and the bridge E=3.45×10 10 N / m 2 , I=1.23m 4 .

[0158] The actual bridge test mainly consists of three parts. The first part is the inherent parameter test of the test vehicle. By applying excitation to the test vehicle, the test vehicle's own frequency is obtained to be 3.00Hz; in order to compare with the vehicle-bridge coupling vibration test results; the second part is the direct measurement test. By placing the sensor directly on the bridge deck, the fundamental frequency of the bridge is quickly extracted, and its value is 8.86Hz; in order to check the transmission performance between the test vehicle signal and the road surface; the third part is the transmission test of the test vehicle. The acceleration signal collected by the test vehicle and the corresponding spectrum diagram are shown in Figure 2. Fig.14 , Fig.15 , Fig.16 and Fig.17 As shown in the figure, it can be seen that the bridge frequency and vehicle frequency can be obtained in the filtered spectrum diagram, which also shows that the vibration transmission of the test vehicle is good.

[0159] According to the above theoretical methods and numerical simulation steps, relevant experiments were carried out: The layout of the measuring points of the first span of Minxie Bridge is shown in the figure below: Fig.18 As shown, two test vehicles acquire signals at each node in a stationary state from left to right at the same distance of 2m. The front vehicle is test vehicle ① and the rear vehicle is test vehicle ②. Due to space limitations, the specific acquisition process can refer to the existing technology.

[0160] The test data collection of the first span of Minxie Bridge was conducted twice, 4 days and 90 days after the completion of the bridge. Since the first test was conducted shortly after the completion of the bridge, it can be considered that the first data was collected when the bridge was in an intact state. First, based on the above test collection steps and analysis methods, the statistical moment curvature difference curve obtained from the two test data of the vehicle-bridge coupling vibration test method and the statistical moment difference curve obtained by the two measuring point data obtained in the actual bridge load test report were compared and verified using the method of the present invention. At the same time, the changes in the node position curves were observed to determine whether the bridge was damaged. Fig.19 Secondly, in order to further analyze the degree of structural damage, an objective function with statistical moment curvature as a parameter is established, and a finite element model is established using the test point data. The statistical moment curvature obtained by the model is used to correct the measured statistical moment curvature to obtain the unit stiffness of the bridge structure. At the same time, the unit stiffness is obtained by using the traditional transmissibility method based on the vehicle-bridge coupling vibration test data in reference to the existing technology and compared. The results are shown in Fig. 20 shown.

[0161] By comparing the statistical moment curvature difference curve obtained from the test data of the vehicle-bridge coupling vibration test method and the statistical moment difference curve obtained from the test data of the actual bridge load test report, it can be seen that the two statistical moment curvature difference curves basically overlap, and the shape is basically a straight line, which is also consistent with the result of the bridge load test report that the bridge is basically intact. At the same time, by using the method of the present invention to establish the objective function with statistical moment curvature as a parameter to correct the finite element model and the traditional transmission rate method to analyze the damage degree identification effect of the bridge, it can be seen that both methods can accurately identify the degree of damage of the bridge, and it can be determined that the bridge is basically undamaged, and the recognition effect of the damage degree identification method proposed by the present invention is closer to the standard value of the stiffness coefficient, especially in the case of complex environmental noise, this method shows a great advantage. Overall, it shows that the method of the present invention has a good effect on the location of damage and the judgment of the degree of damage, and the recognition error is smaller and the noise resistance is stronger.

[0162] 4 Conclusion:

[0163] By establishing the statistical moment curvature difference curve before and after the bridge structure is damaged, and finding the mutation peak from it, it is used as an indicator for determining the location of the structural damage. Then, based on the statistical moment curvature, an objective function is constructed to realize the bridge model correction, thereby obtaining the damage status of the bridge. At the same time, the feasibility of the method is verified through numerical simulation and real bridge tests, and the following conclusions are drawn:

[0164] (5) The bridge damage identification method based on statistical moment curvature can still perform bridge damage identification well under the influence of various factors (unit damage degree, bridge damping ratio, and environmental noise).

[0165] (6) Compared with the flexibility curvature and mode curvature indices, the statistical moment curvature index has higher noise resistance and efficiency. At the same time, by comparing the existing theoretical identification method of bridge damage transmission rate, it is found that for single and multiple bridge damages, the index proposed in the present invention has a better effect on damage location and damage degree judgment, and the identification error is smaller.

[0166] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration, characterized in that: The following steps are involved: Step 1: Use a mobile test vehicle to obtain acceleration signals at corresponding measuring points on the bridge; Step 2: Process the collected acceleration signal and calculate the fourth-order statistical moment of acceleration; Step 3: Calculate the statistical moment curvature through the fourth-order statistical moment of acceleration of each measuring point, and draw a difference curve to identify the damage location; Step 4: The obtained statistical moment curvature is used to obtain the unit stiffness of the bridge through the model correction method, so as to identify the damage degree of the bridge; The step 2 is specifically as follows: When the mean value of the acceleration signal is zero, the second-order acceleration statistical moment can be expressed as: Where: is the second-order statistical moment of the acceleration of vehicle 1 at position d1; is the number of sampling points; is the normal coordinate corresponding to the jth vibration mode; is the i-th sampling point moment; is the j-th order vibration mode; The step three is specifically as follows: Acceleration fourth-order statistical moment index It can be expressed as: Where: is the statistical moment index; The coordinates of the measuring point Then, the central difference method is used to obtain the statistical moment curvature curve for the statistical moment curve. The statistical moment curvature values ​​of each measuring point of the bridge in the previous state are compared. The curvature values ​​of the measuring points in different states are subtracted by formula (26) to draw the statistical moment curvature difference curve along the longitudinal direction of the bridge. The bridge damage position can be obtained by highlighting the changing measuring points based on the statistical moment curvature difference curve. Formula (26) is: (26) Where: is the absolute difference of the statistical moment curvature; is the statistical moment curvature of the first vibration mode of the first-order fundamental frequency signal of the damaged structure at the measuring point i; is the statistical moment curvature of the first vibration mode of the first-order fundamental frequency signal of the undamaged structure at the measuring point i; The step 4 is specifically as follows: An objective function with statistical moment curvature as a parameter is constructed to realize bridge model correction and obtain the damage degree of the bridge.

2. The statistical moment curvature beam bridge damage identification method based on vehicle-bridge coupled vibration according to claim 1 is characterized in that: In step 1, the motion equations of the mobile excitation vehicle and the bridge are: (1) (2) Where: are the vertical acceleration and displacement of the mobile excitation vehicle, respectively; is the vertical displacement of the bridge; for To find the partial derivative with respect to time; for To find the partial derivative with respect to displacement; δ , x and t is the Diktonic function, horizontal displacement and action time; is the uniform mass of the bridge; To test the quality of the vehicle; To test the vehicle stiffness; is the flexural stiffness of the bridge; is the vehicle-bridge interaction force; Using the modal superposition method, the motion equation of the mobile test vehicle can be further obtained using equations (1) and (2): (4) (5) Where: The mass of the test vehicle 1; is the vertical acceleration of test vehicle 1; Damping for test vehicle 1; is the vertical speed of test vehicle 1; is the vertical speed of the bridge; is the location of test vehicle 1; is the stiffness of test vehicle 1; is the vertical displacement of the test vehicle 1; To test the quality of car 2; is the vertical acceleration of test vehicle 2; Damping for test vehicle 2; is the vertical speed of test vehicle 2; is the location of test vehicle 2; To test the stiffness of vehicle 2; It is the vertical displacement of test vehicle 2.

Images