Bridge mode identification method based on vehicle vibration signal

Abstract

The application discloses a bridge mode identification method based on vehicle vibration signals, which comprises the following steps: step one, arranging sensors on the central position of the axle of a measuring vehicle or on the carriage directly above the central position of the axle of the measuring vehicle; step two, leading the measuring vehicle to uniformly drive over the bridge to be measured by a tractor, and recording the vertical acceleration response detected by the sensors during the driving of the measuring vehicle on the bridge to be measured; step three, constructing the balance equation of the vehicle and the bridge, and solving the analytic expression of the vertical acceleration response of the measuring vehicle; step four, obtaining the inherent frequency range of the bridge to be measured through the vertical acceleration response; step five, based on the inherent frequency range of the bridge, separating the bridge mode component from the vertical acceleration response of the measuring vehicle by the zero-phase filtering method; step six, extracting the instantaneous amplitude of each order mode component of the bridge by the Hilbert transform; and step seven, correcting the instantaneous amplitude to obtain the bridge mode immune to the influence of the bridge damping.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge health monitoring, and particularly relates to a bridge mode identification method based on a vehicle vibration signal. BACKGROUND

[0002] Under the background of the vigorous development of a traffic power, more and more bridges are emerging. With the large-area service of the bridge structure, the structural safety and operation and maintenance problems also occur. If not timely discovered and handled, the problems may cause great hidden troubles to the safe service of the bridge. Therefore, it is necessary to monitor the health of the engineering structure to find the damage degree, provide a basis for the reinforcement and repair of the structure, ensure the normal operation of the structure, and protect the safety of people's life and property. However, in the face of a large number of bridge structures, how to realize rapid, economic and accurate state evaluation and damage diagnosis is a key problem to be solved in the management of infrastructure in China.

[0003] Modal parameters (including natural frequency, damping ratio and modal shape) as the inherent properties of the structure are usually used to describe the basic dynamic characteristics of the structure and are widely used in the fields of structural damage identification, finite element model updating and structural health monitoring. Compared with the natural frequency, the change of the modal shape is more sensitive to the damage of the structure and can be used to identify the local / mild damage of the structure, especially the high-order modal shape of the structure. The traditional method for obtaining the modal shape of the structure mainly arranges a series of sensors at different positions along the bridge deck, and reconstructs the modal shape of the bridge from the multiple sets of responses recorded by the sensors by using relevant signal analysis techniques. Due to the limitation of the number of sensors, the spatial resolution of the obtained bridge mode is low, that is, the mode curve is discontinuous, which is often not conducive to the damage detection of the bridge structure.

[0004] In recent years, the bridge state evaluation technology based on vehicle response has developed rapidly. The technology mainly considers installing sensors on a moving test vehicle, recording the vehicle body vibration signals when passing through the bridge, and identifying the modal parameters (natural frequency, damping ratio and modal shape) of the bridge through data analysis. The method is favored by scholars all over the world due to its characteristics of rapidness, economy, ease of operation and strong maneuverability, and its effectiveness and efficiency have been fully verified. However, the method is only suitable for bridges with small structural damping, and cannot be accurately used to identify bridges with large damping. The main reason is that due to the existence of the damping ratio, the envelope of the bridge modal response amplitude separated from the vehicle response will shrink and shift, resulting in that the reconstructed mode curve deviates completely from the theoretical modal shape. In addition, the signal filtering technology used in the traditional technology has phase delay, and the bridge modal response cannot be accurately obtained, which further causes the boundary effect of the extracted modal response amplitude, and interferes with the positioning of the bridge damage by engineers. SUMMARY

[0005] Therefore, the present application aims to provide a bridge mode recognition method based on vehicle vibration signals, which can eliminate the contraction and deviation effects caused by the existence of structural damping ratio and realize accurate identification of the modal vibration mode of the damping bridge.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical solutions.

[0007] A bridge mode recognition method based on vehicle vibration signals comprises the following steps:

[0008] Step one: arranging the sensor at the central position of the measuring vehicle axle or on the carriage located directly above the central position of the measuring vehicle axle;

[0009] Step two: using a tractor to guide the measuring vehicle to drive at a constant speed through the bridge to be measured, and recording the vertical acceleration response detected by the sensor during the driving of the measuring vehicle on the bridge to be measured ;

[0010] Step three: constructing the balance equation of the vehicle and the bridge to obtain the analytical expression of the vertical acceleration response of the measuring vehicle ;

[0011] Step four: obtaining the natural frequency range of the bridge to be measured through the vertical acceleration response ;

[0012] Step five: based on the natural frequency range of the bridge, using the zero-phase filtering method to separate the bridge modal component from the vertical acceleration response of the measuring vehicle ; ;

[0013] Step six: using Hilbert transform to extract the instantaneous amplitude of each order modal component of the bridge :

[0014] Step seven: correcting the instantaneous amplitude , to obtain the bridge mode immune to the influence of the bridge damping.

[0015] Further, in the step three, the balance equation of the vehicle and the bridge is:

[0016]

[0017]

[0018] wherein, is the unit length mass of the bridge; is the damping coefficient of the bridge; is the bending stiffness of the bridge; represents the contact force between the vehicle and the bridge; is the Dirac function; to measure the mass of the vehicle; to measure the stiffness of the vehicle; and respectively represent the vertical displacement of the bridge and the measuring vehicle; represents the first order derivative of ; represents the second order derivative of ; represents the fourth order derivative of x; represents the vertical acceleration response of the measuring vehicle; represents the distance of the vehicle from the entry point of the bridge; represents time; represents the speed of the measuring vehicle on the bridge; is the contact displacement between the bridge and the vehicle;

[0019] the analytical expression of the vertical acceleration response obtained by solving is:

[0020]

[0021] wherein, represents the speed parameter; represents the static displacement caused by the vehicle-induced vibration of the bridge; represents the length of the bridge; represents the gravitational acceleration; represents the modal order of the bridge; , and respectively represent the natural frequency, the damped frequency and the damping ratio of the measured bridge; is the coefficient related to the vibration replication of the measured bridge; represents the phase angle; represents the natural frequency of the vehicle.

[0022] Further, in the fourth step, the natural frequency of the measured bridge is represented as:

[0023]

[0024] wherein, represents the natural frequency of the measured bridge; represents the frequency; represents the vertical acceleration response of the bridge; is the discrete sampling point from 0 to ; is the total length of the signal to be analyzed; represents the imaginary unit.

[0025] Further, in the step five, the zero-phase filtering method process is as follows:

[0026] The sequence is input to the filter to generate a filtered signal :

[0027]

[0028] The filtered signal is flipped to obtain a signal :

[0029]

[0030] The signal is inverse filtered to obtain a signal :

[0031]

[0032] The signal is flipped to obtain an output signal :

[0033]

[0034] The vertical acceleration response is processed by the zero-phase filtering method to obtain a zero-phase output signal, i.e., the modal components of each order of the bridge :

[0035]

[0036] wherein, is defined as the corresponding transform in the time domain.

[0037] Further, in the step six, the instantaneous amplitude is expressed as:

[0038]

[0039] wherein, represents the transform pair of the modal components of each order of the bridge .

[0040] Further, in the step seven, the correction method of the instantaneous amplitude includes the following steps:

[0041] 71) Perform a reflection transform on the instantaneous amplitude on the axis to obtain a reflection amplitude :

[0042]

[0043] 72) the obtained reflection amplitude Perform a translation transformation: that is, shift the reflection amplitude along the axis to the right by L / v units of length, obtaining a translation amplitude :

[0044]

[0045] 73) since and have the same range of values, replace with , multiplying the instantaneous amplitude by the translation amplitude , obtaining a modified bridge mode shape :

[0046]

[0047] wherein represents the amplitude of the modified mode shape.

[0048] The beneficial effects of the present application are:

[0049] The present application is based on a bridge mode shape identification method for vehicle vibration signals, by arranging sensors on the central position of the vehicle axle or on the vehicle compartment above the central position of the vehicle axle, during the process of guiding the measuring vehicle along the measured bridge at a uniform speed, the vertical acceleration response can be measured by the sensors, and through the balance equation of the vehicle and the bridge, the analytical expression of the vertical acceleration response is obtained, then, the bridge modal component separated from the vertical acceleration response of the measuring vehicle is used to eliminate the phase distortion existing in the separated bridge modal response, to obtain a "high-fidelity" bridge component response; after using Hilbert transform to extract the instantaneous amplitude of each order modal component of the bridge , the instantaneous amplitude is corrected to eliminate the shrinkage and offset effects caused by the existence of structural damping ratio, to realize the accurate identification of the damping bridge modal shape, so as to further use the bridge modal shape for bridge damage identification. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to make the purpose, technical scheme and beneficial effects of the present application clearer, the present application provides the following drawings for illustration:

[0051] Figure 1Flow chart of bridge mode identification method based on vehicle vibration signal of the present application;

[0052] Figure 2 Principle diagram of bridge mode correction system embodiment;

[0053] Figure 3 Structural schematic diagram of measurement vehicle system;

[0054] Figure 4 Mathematical model of measured bridge;

[0055] Figure 5 Bridge mode identified under different structural damping ratio conditions;

[0056] Figure 6 Bridge mode identified under different vehicle speed conditions;

[0057] Figure 7 Bridge mode identified under different bridge high order (second, third order) conditions;

[0058] Figure 8 Bridge mode identified under three-span continuous bridge conditions. DETAILED DESCRIPTION

[0059] The present application will be further described below in conjunction with the drawings and specific embodiments, so that those skilled in the art can better understand the present application and implement it, but the embodiments are not limiting to the present application.

[0060] As shown in Figure 1 , the bridge mode identification method based on vehicle vibration signal of the present embodiment comprises the following steps:

[0061] Step one: the sensor 15 is arranged at the central position of the vehicle axle 14 of the measurement vehicle 10 or on the vehicle compartment 16 directly above the central position of the vehicle axle of the measurement vehicle 10. The sensor 15 of the present embodiment adopts an acceleration sensor, and the sensor 15 is arranged at the central position of the vehicle axle 14 of the measurement vehicle 10.

[0062] Step two: the towing vehicle 11 is used to guide the measurement vehicle 10 to drive at a constant speed through the bridge to be measured, and the vertical acceleration response detected by the sensor during the driving of the measurement vehicle on the bridge to be measured is recorded. .

[0063] Step three: the balance equation of the vehicle and the bridge is constructed, and the analytical expression of the vertical acceleration response of the measurement vehicle is solved. .

[0064] Specifically, the balance equation of the vehicle and the bridge is:

[0065]

[0066]

[0067] where, is the unit length mass of the bridge; is the damping coefficient of the bridge; is the bending stiffness of the bridge; represents the contact force between the vehicle and the bridge; is the Dirac function; is the mass of the measurement vehicle; is the stiffness of the measurement vehicle; and are the vertical displacements of the bridge under test and the measurement vehicle, respectively; represents the first order derivative of ; represents the second order derivative of ; represents the fourth order derivative of x; represents the vertical acceleration response of the measurement vehicle; represents the distance of the vehicle from the bridge entry point; represents time; represents the speed of the measurement vehicle on the bridge under test; is the contact displacement between the bridge and the vehicle;

[0068] the analytical expression of the vertical acceleration response obtained by solving is:

[0069]

[0070] where, is the velocity parameter; is the static displacement generated by the vehicle-induced bridge vibration; represents the length of the bridge; represents the acceleration due to gravity; represents the modal order of the bridge; , and are the natural frequency, the damped frequency and the damping ratio of the bridge under test, respectively; is the coefficient related to the vibration replication of the bridge under test; represents the phase angle; represents the natural frequency of the vehicle.

[0071] Step four: obtain the natural frequency range of the bridge under test through the vertical acceleration response .

[0072] Specifically, the natural frequency of the bridge under test is represented as:

[0073]

[0074] wherein, represents the natural frequency of the bridge under test; represents the frequency; represents the vertical acceleration response of the bridge; is the discrete sampling point from 0 to ; is the total length of the signal to be analyzed; represents the imaginary unit.

[0075] Step five: based on the natural frequency range of the bridge, the bridge modal components are separated from the measured vertical acceleration response of the vehicle using a zero-phase filtering method . .

[0076] Specifically, the process of the zero-phase filtering method is as follows:

[0077] input the sequence to the filter to generate the filtered signal :

[0078]

[0079] flip the filtered signal to obtain the signal :

[0080]

[0081] inverse filter the signal to obtain the signal :

[0082]

[0083] flip the signal to obtain the output signal :

[0084]

[0085] After the vertical acceleration response is processed using the zero-phase filtering method, the zero-phase output signal, i.e., the modal components of the bridge :

[0086]

[0087] wherein, is defined as the corresponding transform in the time domain.

[0088] Step six: Extracting the instantaneous amplitude of each modal component of the bridge by using Hilbert transform .

[0089] Specifically, the instantaneous amplitude is expressed as:

[0090]

[0091] wherein, represents the transform pair of each modal component of the bridge.

[0092] It can be seen that the obtained instantaneous amplitude contains the damping term of the bridge which will cause the shrinkage and offset effect on the bridge mode shape.

[0093] Step seven: correcting the instantaneous amplitude obtained in the previous step to obtain the bridge mode shape immune to the influence of the bridge damping.

[0094] Specifically, in the present embodiment, the correction method of the instantaneous amplitude includes the following steps:

[0095] 71) Perform reflection transform on the instantaneous amplitude on the axis to obtain the reflection amplitude :

[0096]

[0097] 72) Perform translation transform on the obtained reflection amplitude : that is, translate the reflection amplitude to the right along the axis by L / v unit length to obtain the translation amplitude :

[0098]

[0099] 73) Since and have the same value range, replace with , and multiply the instantaneous amplitude by the translation amplitude to obtain the corrected bridge mode shape :

[0100]

[0101] wherein, represents the amplitude of the corrected mode shape.

[0102] The expression of the bridge mode shape As can be seen from the expression of the bridge mode shape, the correction process of the bridge mode shape does not require additional bridge information, such as the damping ratio which is difficult to accurately identify; the bridge mode shape identification only requires the vehicle body response recorded by a single sensor, and the continuous (high-resolution) bridge mode shape can be accurately reconstructed through the above transformation.

[0103] As Figure 2 shown, it is a structural schematic diagram of a bridge mode shape identification system suitable for the bridge mode shape identification method based on vehicle vibration signals according to the present application. The bridge mode shape identification system comprises a field measurement system, a data analysis processing platform and a data output and display terminal.

[0104] In the embodiment, the field measurement system comprises a measurement vehicle system, a data acquisition module, a data conversion module, a data communication module and a data storage module. The measurement vehicle system of the embodiment is used for real-time measurement of vertical acceleration response data, the data acquisition module acquires the vertical acceleration response data measured by the sensor, the data conversion module performs data conversion on the acquired vertical acceleration response data, and the data communication module transmits the converted vertical acceleration response data to the data storage module for storage. As Figure 3 shown, the measurement vehicle system of the embodiment comprises a measurement vehicle 10 and a towing vehicle 11, the towing vehicle 11 is used for guiding the movement of the measurement vehicle 10, and the measurement vehicle 10 can rotate relative to the towing vehicle 11 around a rotating shaft 12 and can move relative to the towing vehicle 11 along a sliding shaft 13, the rotating shaft 12 and the sliding shaft 13 are perpendicular to each other. In the embodiment, the rotating shaft 12 is rotationally connected with the towing vehicle 11, the rotating shaft 12 is provided with a sliding sleeve, the sliding shaft 13 is slidingly connected with the sliding sleeve, and the sliding shaft 13 is fixedly connected with the measurement vehicle 10. The measurement vehicle 10 comprises a vehicle compartment 16, a vehicle axle 14 is installed on the vehicle compartment 16, the vehicle axle 14 is perpendicular to the rotating shaft 12 and the sliding shaft 13, and the sliding shaft 13 is fixedly installed on the vehicle compartment 16. The vehicle axle 14 is arranged at a central position of the vehicle axle 14 and is provided with a sensor 15 for acquiring acceleration data of the measurement vehicle 10 during driving on the measured bridge. Of course, in other embodiments, the sensor 15 can also be arranged on the vehicle compartment 16 directly above the central position of the vehicle axle 14.

[0105] In the embodiment, the data analysis processing platform is used for bridge mode shape identification according to the acquired vertical acceleration response data.

[0106] In the embodiment, the data output and display terminal is used for real-time output and display of the calculation results of the data analysis processing platform.

[0107] The bridge mode shape identification method based on vehicle vibration signals according to the present application will be described below in combination with specific examples.

[0108] In the numerical verification, the Figure 4Mathematical model of the measured bridge. Figure 4 The parameters of the measured bridge in the simulation are set as follows: the bridge length L = 25 m, the cross-sectional size A = 3.2 m 2 , the bridge density ρ = 4800 kg / m 3 , and the elastic modulus E = 2.75 × 10 10 N / m 2 . The parameters of the measurement vehicle are set as follows: the vehicle stiffness k v = 200 kN / m, the vehicle mass m v = 14,000 kg, and the moving speed v = 2 m / s. The theoretical values of the first two order frequencies of the bridge can be calculated as 1.39 Hz and 5.56 Hz, respectively, by the given bridge parameters.

[0109] To verify the universality of the bridge mode identification method based on the vehicle vibration signal of the embodiment, different bridge damping ratios, different moving speeds, different modal orders, and different bridge structures are verified by numerical simulation. Specifically, the bridge roughness identification under the following four working conditions is simulated in the embodiment:

[0110] Working condition one: the identified bridge mode under different structural damping ratios, as shown in FIG. 1; Figure 5

[0111] Working condition two: the identified bridge mode under different vehicle speeds, as shown in FIG. 2; Figure 6

[0112] Working condition three: the identified bridge mode under different orders of the bridge, as shown in FIG. 3; Figure 7

[0113] Working condition four: the identified bridge mode under the condition of a three-span continuous bridge, as shown in FIG. 4. Figure 8

[0114] From the numerical verification results of the four working conditions, it can be seen that the mode results obtained by the bridge mode correction system based on the vehicle vibration signal of the embodiment have high consistency with the theoretical values, and the obtained mode has extremely high spatial resolution, which can be used as a reliable index for bridge damage detection. It is proved that the bridge mode correction system based on the vehicle vibration signal of the embodiment has wide applicability, the identification process is efficient, the identification process is simple, the identification result is accurate, and it can provide new technical support for large-scale bridge structure mode identification, serve bridge health monitoring, operation management and maintenance.

[0115] ​​​​The above-described embodiments are merely preferred embodiments of the present application, and the protection scope of the present application is not limited thereto. Any equivalent substitutions or transformations made by those skilled in the art based on the present application are within the protection scope of the present application. The protection scope of the present application is subject to the claims.

Claims

1. A bridge modal identification method based on vehicle vibration signals, characterized in that: The method comprises the following steps: Step one: arranging the sensor at the central position of the axle of the measuring vehicle or on the carriage right above the central position of the axle of the measuring vehicle; Step two: the measuring vehicle is driven at a constant speed by the tractor to pass through the bridge to be measured, and the vertical acceleration response detected by the sensor is recorded during the driving of the measuring vehicle on the bridge to be measured ; Step three: Construct the equilibrium equation of the vehicle and the bridge, and solve to obtain the vertical acceleration response of the measuring vehicle analytical expression; Step four: obtaining the natural frequency range of the bridge under test by vertical acceleration response obtaining the natural frequency range of the bridge under test; Step five: Using zero-phase filtering method to separate the bridge modal components from the measured vehicle vertical acceleration response based on the bridge natural frequency range ;​ Step six: Extracting the instantaneous amplitude of each modal component of the bridge by using Hilbert transform : Step seven: Correcting the instantaneous amplitude The result is the bridge mode shape with the effect of the immunization bridge damping.

2. The bridge mode identification method based on vehicle vibration signals according to claim 1, characterized in that: In the step three, the balance equation of the vehicle and the bridge is: wherein, is the unit length mass of the bridge; is the damping coefficient of the bridge; is the bending stiffness of the bridge; denotes the contact force between the vehicle and the bridge; is the Dirac function; is the mass of the measurement vehicle; is the stiffness of the measurement vehicle; and are the vertical displacements of the bridge under test and the measurement vehicle, respectively; denotes the first derivative of ; denotes the second derivative of ; denotes the fourth derivative of x; denotes the vertical acceleration response of the measurement vehicle; denotes the distance of the vehicle from the bridge entry point; denotes time; denotes the speed of the measurement vehicle on the bridge under test; is the contact displacement between the bridge and the vehicle; The analytical expression of the vertical acceleration response obtained by solving is wherein, represents a velocity parameter; represents a static displacement generated by vehicle-induced bridge vibration; represents a length of the bridge; represents a gravitational acceleration; represents a modal order of the bridge; , and are, respectively, a natural frequency, a damped frequency, and a damping ratio of the measured bridge; is a coefficient related to vibration replication of the measured bridge; represents a phase angle; represents a natural frequency of the vehicle.

3. The bridge mode identification method based on vehicle vibration signal according to claim 2, characterized in that: In the step four, the natural frequency of the measured bridge is represented as: wherein, represents the natural frequency of the bridge under test; represents the frequency; represents the vertical acceleration response of the bridge; is the total length of the signal to be analyzed; are the discrete sampling points from 0 to represents the imaginary unit.​ 4. The bridge mode identification method based on vehicle vibration signal according to claim 3, characterized in that: In the step five, the process of the zero-phase filter method is: The sequence is input to a filter to generate a filtered signal : on the filtered signal reversing, to obtain a signal : to the signal performing inverse filtering on the signal : to the signal is inverted to obtain an output signal : The vertical acceleration response is obtained After processing by the zero-phase filtering method, the output signal of zero phase, i.e. the modal components of the bridge are obtained : wherein defined as the corresponding transform.

5. The bridge mode identification method based on vehicle vibration signal according to claim 4, characterized in that: In step six, the instantaneous amplitude is represented as: wherein denotes the transform pair of the bridge's individual modal components of the bridge.

6. The bridge mode identification method based on vehicle vibration signal according to claim 4, characterized in that: The step seven, the instantaneous amplitude The correction method of the instantaneous amplitude comprises the following steps: 71) on the instantaneous amplitude In Performing the reflection transform on the axis, the reflected amplitude : 72) the resulting reflection amplitude perform a translation transform: i.e. shift the reflection amplitude along by L / v units of length to the right along the axis, resulting in a translated amplitude : 73) because and having the same range of values, are replaced by the instantaneous amplitude is multiplied by the translation amplitude to obtain the modified bridge mode shape :​ wherein, represents the amplitude of the modified mode shape.

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