JP2016194442A - Method of evaluating specific frequency variations of railway bridges - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method of evaluating specific frequency variations of railway bridges by which accurate evaluation can be done, in evaluating cracks in the underside of a concrete-built railway bridge by using a TV-VAR model, by preventing infiltration of errors invited by vibration amplitude variations.SOLUTION: By a method of evaluating specific frequency variations of railway bridges, the vibration waveform of the main girder of a concrete-built railway bridge is measured; the measured vibration waveform is subjected to FFT processing, peak frequency extraction processing and band-pass filter processing to generate a mode waveform; the envelope of the generated mode waveform is calculated; a standard mode waveform is so generated as to keep the amplitude constant all the time on the basis of the calculated envelope; and on the basis of the generated standard mode waveform, the specific frequency variation of the railway bridge is evaluated by using a TV-VAR model.SELECTED DRAWING: Figure 5

Description

  The present invention relates to a method for evaluating the amount of change in the natural frequency of a railway bridge, and more particularly, to a method for evaluating the amount of change in the natural frequency of a railway bridge that can contribute to detection of cracks generated on the lower surface of a main girder of a concrete railway bridge.

  Conventionally, concrete railway bridges, such as reinforced concrete railway bridges, prestressed concrete railway bridges, and partial prestressed concrete railway bridges, have been placed on the underside of the main girder due to repeated loads over many years, loading of significant loads, or deterioration. Cracks may occur. When cracks are detected, repair and reinforcement work is performed as necessary, and maintenance of the concrete railway bridge is performed.

  The presence or absence of cracks on the lower surface of the main girder of the concrete railway bridge is determined by proximity visual inspection in which an inspector approaches the lower surface of the main girder and visually observes, or as shown in Patent Document 1, the range in which cracks occur The image is picked up using image pickup means such as a CCD camera and image processing is performed.

  Crack detection on the underside of the main girder of a concrete railway bridge using visual or imaging means can detect cracks that are always open, but if cracks open only when large amplitudes occur due to load loading, etc. The presence or absence of cracks cannot be confirmed, and there is a drawback that requires a skilled inspector and complicated inspection equipment. For this reason, it is desired to be able to determine the presence or absence of cracks and a decrease in cross-sectional rigidity from a deflection response that can be measured remotely, so that the maintenance and management of the concrete railway bridge can be performed efficiently.

By the way, since it is known that the natural frequency of a concrete railway bridge has a predetermined relationship with the cross-sectional rigidity, a change in the natural frequency due to a change in the effective cross-section due to a crack is detected to detect a crack. It has been tried. In other words, the natural frequency of a concrete railway bridge with cracks on the underside of the main girder of the concrete railway bridge varies depending on whether the concrete railway bridge is an upward vibration or a downward vibration. Attempts have been made to detect cracks.
Note that the fact that the natural frequency of the concrete railway bridge has a predetermined relationship with the cross-sectional rigidity will be described in detail in the following “Description of Embodiments”.

  In addition, as a method for evaluating the fluctuation of the natural frequency, as shown in Non-Patent Document 1, a time change (Time Variing: Time Variant :) is applied to an AR coefficient matrix of a multivariate autoregressive model (VAR Model). TV-VAR models that allow TV) are known. For this reason, it is considered that this TV-VAR model is used for detecting cracks on the lower surface of the main girder of a concrete railway bridge.

JP 2004-294318 A

Hirooka Matsuoka, Kiyoyuki Kaido: Identification of bridge frequency during train running by hierarchical Bayesian estimation of TV-VAR model, Proceedings of Japan Society of Civil Engineers, A1, Vol. 68, no. 3, pp. 738-753, 2012.12.

However, when wavelet transform or continuous Fourier transform is used to detect changes in the natural frequency of a concrete railway bridge with cracks on the lower surface of the main girder of the above-mentioned concrete railway bridge, the natural frequency fluctuation interval is used. However, there was a problem that it was too short to be evaluated accurately.
When the above TV-VAR model is used to detect cracks on the bottom face of the main girder of a concrete railway bridge, errors caused by changes in amplitude are mixed in when the detected waveform is used directly for accurate evaluation. There was a problem that could not be done.

  Therefore, the present invention has been made to solve the above-described problems. The natural frequency of a concrete railway bridge is measured to detect cracks on the lower surface of the main girder of the concrete railway bridge using a TV-VAR model. It is an object of the present invention to provide a method for evaluating the amount of change in the natural frequency of a railway bridge that can be accurately evaluated while preventing errors due to amplitude changes.

  In order to achieve the above object, the method for evaluating the amount of change in the natural frequency of a railway bridge according to the present invention is to detect cracks generated on the bottom surface of the main girder of a concrete railway bridge from the change in the natural frequency of the concrete railway bridge. A method for evaluating a change amount of a natural frequency of a railway bridge used, wherein a vibration waveform of a main girder of the concrete railway bridge is measured, and the measured vibration waveform is subjected to FFT processing, peak frequency extraction processing, and bandpass filter processing. To generate a mode waveform, calculate an envelope of the generated mode waveform, generate a standard mode waveform so that the amplitude is always constant based on the calculated envelope, and generate the mode waveform Based on the measured standard mode waveform, the change in the natural frequency of the railway bridge was evaluated using a model that allowed temporal changes in the autoregressive coefficient matrix of the multivariate autoregressive model. It is characterized in that.

  In the present invention, the waveform used in a model that allows temporal changes in the autoregressive coefficient matrix of the multivariate autoregressive model (hereinafter referred to as the TV-VAR model) is such that the amplitude of the measured vibration waveform is always constant. Thus, since the pre-processed standard mode waveform is obtained, it is possible to prevent an error due to an amplitude change and to obtain a sufficient evaluation time to perform the TV-VAR model evaluation. Accurate evaluation can be performed. Therefore, the presence or absence of cracks on the lower surface of the main girder of the concrete railway bridge and the degree of the cracks can be accurately detected using the TV-VAR model evaluation.

  Further, in the method for evaluating the variation in the natural frequency of the railway bridge according to the present invention, the measurement of the vibration waveform of the main girder of the concrete railway bridge is carried out from the vibration waveform obtained when the train travels on the concrete railway bridge. It is characterized by being obtained by cutting out the subsequent vibration waveform.

  The present invention has an advantage that the vibration waveform of the main girder can be measured using the traveling of the train.

According to the railway bridge natural frequency variation evaluation method of the present invention, the waveform used in the TV-VAR model is obtained by performing FFT processing, peak frequency extraction processing, and bandpass filter processing on the waveform after passing the train. Generate a waveform, and then calculate the envelope of the generated mode waveform, and the standard mode waveform generated so that the amplitude is always constant based on the calculated envelope. Since it is processed, it is possible to prevent an error due to a change in amplitude and to obtain a sufficient evaluation time and perform a TV-VAR model evaluation. Therefore, it is possible to accurately evaluate the amount of change in the natural frequency. .
Therefore, it is possible to accurately detect the presence and degree of cracks on the bottom surface of the main girder of a concrete railway bridge using the TV-VAR model evaluation, and thereby to maintain and manage the concrete railway bridge more efficiently. Can do. In addition, by using the results obtained by this evaluation method, it is possible to perform a concrete railway bridge simulation during traveling of a vehicle (train) with higher accuracy.

It is a figure for demonstrating that the natural frequency of a concrete railway bridge has a predetermined relationship with cross-sectional rigidity, Comprising: (a) is a figure which shows the state at the time of non-loading, (b) is a center cross-section of a girder It is a figure which shows force. It is a figure for demonstrating that the natural frequency of a concrete railway bridge has a predetermined relationship with cross-sectional rigidity, (a) is a figure which shows the state at the time of loading or a lower side amplitude, (b) These are figures which show a girder center section force. It is a figure for demonstrating that the natural frequency of a concrete railway bridge has predetermined | prescribed relationship with cross-sectional rigidity, Comprising: (a) is a figure which shows the state at the time of an upper side amplitude, (b) is a cross-section in the center of a girder It is a figure which shows force. It is a deflection waveform figure accompanying passage of a train. It is an evaluation flow of the variation | change_quantity evaluation method of a railway bridge natural frequency by embodiment of this invention. (A) is a figure showing a peak frequency, (b) is a figure showing the zone of a band pass filter. It is a mode waveform diagram by peak estimation based on a spectrum and bandpass filter processing. (A) is a figure which shows a mode waveform and an envelope, (b) is a standard mode waveform figure which always made the amplitude constant. It is based on the TV-VAR model, (a) is a simulated waveform diagram when the main digit is assumed to be healthy, and (b) is a diagram showing an estimated time series at that time. According to the TV-VAR model, (a) is a simulated waveform diagram when it is assumed that the main girder is cracked, and (b) is a diagram showing a time series estimated at that time. It is explanatory drawing which shows the preparation model of a simulated waveform.

  Before describing the embodiment of the method for evaluating the variation amount of the natural frequency of the railway bridge according to the present invention, in order to facilitate understanding of the present invention, the natural frequency of the concrete railway bridge has a predetermined relationship with the cross-sectional rigidity. This will be described with reference to FIGS.

  FIG. 1A, FIG. 2A, and FIG. 3A show a concrete rail bridge 1 having a predetermined length. Both ends of the main girder 2 of the concrete railway bridge 1 are respectively placed on the pier 3 and a predetermined depth is formed on the lower surface of the central portion of the main girder 2 in the length direction (left and right direction on the paper surface). Sano cracks C are formed.

1 (a) and 1 (b) show a non-loading state in which no train is approaching the concrete railway bridge 1. In this state, the crack C is closed, and the entire section is in an effective state. It is shown.
2 (a) and 2 (b) show a loaded state in which a train (not shown) has reached the concrete railway bridge 1 and a state in which the main girder 2 vibrates downward due to vibration accompanying the passage of the train. In this state, since the crack C is opened, it is shown that the cross section corresponding to the crack C is in an invalid state.
And FIG. 3 (a), (b) has shown the state which the main girder 2 is vibrating upwards in the state which is vibrating after the train passes from the concrete railway bridge 1, In this state, Since the crack C is closed, it is shown that the entire section is in an effective state.

FIG. 4 shows an example of a deflection waveform (vibration waveform) accompanying the passage of a train measured by installing an accelerometer on the concrete railway bridge 1 described above. This vibration waveform shows that the train passes through the concrete railway bridge 1 in 4 seconds, and the vibration is measured for 8 seconds after the train passes. Therefore, it can be seen that the vibration at the lower amplitude shown in FIG. 2 and the vibration at the upper amplitude shown in FIG. 3 are repeated for 8 seconds after the train passes. That is, the effective cross section of the main girder 2 of the concrete railway bridge 1 has changed during these 8 seconds.
The waveform shown in FIG. 4 is obtained when the bridge natural frequency is 2.8 Hz and the train traveling speed is 250 km / h.

  By the way, the natural frequency of the concrete railway bridge 1, that is, the natural frequency f of the main girder 2 is expressed by the following equation (1).

  Here, in the equation (1), EI is the cross-sectional rigidity, E is the longitudinal elastic modulus (Young's modulus), I is the cross-sectional secondary moment, L is the span, and m is the unit length mass.

  From the equation (1), it can be seen that when there is a crack C on the lower surface of the main girder 2, the natural vibration changes because I changes between the vibration at the upper amplitude and the vibration at the lower amplitude. Therefore, if the difference between the natural frequency related to the upper vibration and the natural frequency related to the lower vibration is known from the deflection response of the main girder 2, whether or not the crack C is generated on the lower surface of the main girder 2 is determined. Can be determined. The railway bridge natural frequency variation evaluation method according to the present invention is based on the knowledge of the difference from this natural frequency.

  Next, the railway bridge natural frequency variation evaluation method according to the present embodiment will be described with reference to the evaluation flow shown in FIG. 5 and FIGS. In addition, the specific operation | work of each process (each step S mentioned later) of the evaluation flow shown in FIG. 5 is performed using a computer.

  First, in the method for evaluating the amount of change in the natural frequency of a railway bridge according to the present embodiment, a deflection waveform (vibration waveform) is read (step S1 (hereinafter, step is referred to as “step S”). Reading of the measurement value measured by the accelerometer installed on the concrete railway bridge to be detected is performed during the passage of the train and for a predetermined time after the passage of the train, as shown in FIG. A vibration waveform (sometimes simply referred to as “waveform”) is captured.

  Next, in step S2, a mode waveform is calculated based on the waveform read in step S1 described above. In the calculation of the mode waveform, a waveform after passing through the train, that is, a portion of the waveform that is not affected by the load related to the train (vehicle) is cut out from the read waveform (step S21).

Then, the waveform after the train pass cut out, FFT (Fourier transform) after (Step S23), extraction of the peak frequency _{f 0} is performed (see step S23, FIG. 6 (a)). Then, a bandpass filter is set based on the extracted peak frequency f ₀ (see S24, FIG. 6B). Here, the passband f of the bandpass filter is 0.8 f ₀ <f <1.2 f ₀ . Then, filtering is performed using the set bandpass filter (step S25), and a mode waveform is generated (step S26, see FIG. 7).

Next, in step S3, a standardized mode waveform is generated based on the mode waveform generated in step S2. In the generation of the standardized mode waveform, the mode waveform is subjected to Hilbert transform (step S31), and an envelope is generated (see step S32, FIG. 8A).
After step S32, the mode waveform at each time point is divided by the generated envelope (step S33) to generate a standard mode waveform whose amplitude is always “1” (see step S34, FIG. 8B). ).

  Next, in step S4, the natural frequency using a model (TV-VAR model) that allows temporal change in the autoregressive coefficient matrix of the multivariate autoregressive model based on the standard mode waveform generated in step S3. Variation is calculated. That is, in calculating the fluctuation of the natural frequency, a change in the natural frequency is estimated based on the TV-VAR model using a standard mode waveform whose amplitude is always constant (“1” in the illustrated example) (step S41). ), A time series of natural frequencies is calculated from the estimation (step S42).

  Here, FIG. 9A shows a simulated waveform obtained by estimating a standard mode waveform based on the TV-VAR model assuming that no cracks are generated on the lower surface of the main girder. b) shows the logical spectrum of the created waveform. As can be seen from FIG. 9B, the natural frequency when this healthy main girder is assumed is constant (2.8 Hz in the illustrated example) regardless of the amplitude.

  FIG. 10A shows a simulated waveform obtained by estimating a standard mode waveform based on the TV-VAR model assuming that a crack is generated on the lower surface of the main girder. FIG. The logical spectrum of the created waveform is shown. As shown in FIG. 10B, the natural frequency when assuming the main girder having the crack is that the natural frequency decreases (the upper end of the amplitude is constant) as the amplitude increases downward. Recognize. This is also shown in the simulated waveform creation model of the TV-VAR model shown in FIG.

Then, in step S5, with the natural frequency f _d at the lower vibration when vibrating the lower side it is extracted in time series of the original natural frequency at the upper vibration when vibrating the upper The number f _u is extracted, and the natural frequency f _d at the time of the lower side vibration is divided by the natural frequency f _u at the time of the upper side vibration to obtain the rate of change r _f of the natural frequency (r _f = f _d / _Fu ).

By the way, the fluctuation factor of the natural frequency of the main girder is only the secondary moment I of the cross section as shown in the above-described equation (1). Can be detected. Therefore, in step S6, by squaring the variation rate r _f of the natural frequency determined in step S5 described above, rate of decrease in the apparent second moment of the main girder due is calculated for cracking . And the presence or absence of the crack of the main girder lower surface and the extent of the crack are detected from this decreasing rate.

  Thus, in the railway bridge natural frequency variation evaluation method according to the present embodiment, as shown in FIG. 5, the waveform used in the TV-VAR model is obtained by performing FFT processing on the waveform after passing through the train, and the peak frequency. A mode waveform is generated by performing extraction processing and bandpass filter processing, and then an envelope of the generated mode waveform is calculated, and the amplitude is always constant based on the calculated envelope Since the pre-processing is performed so that the generated standard mode waveform is obtained, it is possible to prevent an error due to a change in amplitude and to obtain a sufficient evaluation time to perform the TV-VAR model evaluation. Accurate evaluation of the amount of change in the number can be performed.

  Therefore, it is possible to accurately detect the presence and degree of cracks on the bottom surface of the main girder of a concrete railway bridge using the TV-VAR model evaluation, and thereby to maintain and manage the concrete railway bridge more efficiently. Can do. In addition, by using the results obtained by this evaluation method, it is possible to perform a concrete railway bridge simulation during traveling of a vehicle (train) with higher accuracy.

As mentioned above, although embodiment of the change evaluation method of the natural frequency of a railway bridge by this invention was described, this invention is not limited to said embodiment, It can change suitably in the range which does not deviate from the meaning. It is.
For example, in the above example, the waveform that is the basis for the calculation of the mode waveform is cut out from the read waveform after passing the train, but the impact for measurement using a weight or the like is applied to the concrete railway bridge. It can also be a vibration waveform obtained when applied.

  In addition, the method for evaluating the amount of change in the natural frequency of the railway bridge according to the present embodiment is applied to any object whose cross-sectional rigidity (EI) is changed by cracking, although the object to be detected is a concrete railway bridge. Therefore, in the present invention, the term “railway bridge” includes such a structure.

1 concrete railway bridge 2 main girder 3 pier C crack

Claims (2)

A method for evaluating the amount of change in the natural frequency of a railway bridge used when detecting cracks occurring on the underside of the main girder of a concrete railway bridge from the change in the natural frequency of the concrete railway bridge,
Measure the vibration waveform of the main girder of the concrete railway bridge,
The measured vibration waveform is subjected to FFT processing, peak frequency extraction processing, and bandpass filter processing to generate a mode waveform,
Calculate the envelope of the generated mode waveform, and generate a standard mode waveform so that the amplitude is always constant based on the calculated envelope,
A railway that evaluates a change amount of the natural frequency of the railway bridge using a model that allows a temporal change in an autoregressive coefficient matrix of a multivariate autoregressive model based on the generated standard mode waveform. Method for evaluating the amount of change in bridge natural frequency   The measurement of the vibration waveform of the main girder of the concrete railway bridge is obtained by cutting out the vibration waveform after passing through the train from the vibration waveform obtained when a train travels on the concrete railway bridge. The change evaluation method of the natural frequency of the railway bridge described in 1.

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