JP2021098967A - Mode characteristics estimation method of bridge and mode characteristics estimation system thereof - Google Patents

Abstract

To provide a mode characteristics estimation method of bridge capable of precisely estimating mode characteristics of a bridge while separating the vibration components caused by moving bodies that move on the bridge, and a mode characteristics estimation system thereof.SOLUTION: The mode characteristics estimation method is a method of estimating the mode characteristics of bridge B. In a mode characteristic estimation step, vibration components of vibrations of the bridge B caused by a train T are separated from the vibration components of the bridge B based on the vibration waveform of the bridge B when the train T moves on bridge B, and mode characteristics of the bridge B are estimated. In the mode characteristic estimation step, defining the load of the moving train T, which is an external force as an exogenous variable Am, the mode characteristics of the bridge B is estimated by using a hierarchical Bayesian estimation method for time-varying autoregressive (TV-ARX) models with exogenous variables that allow time-varying parameters. In the mode characteristic estimation step, the natural frequency of the bridge B and/or mode fluctuation of the attenuation ratio is estimated.SELECTED DRAWING: Figure 7

Description

The present invention relates to a bridge mode characteristic estimation method for estimating a bridge mode characteristic and a mode characteristic estimation device thereof.

Dynamic-Bridge interaction (hereinafter referred to as VBI) with a traveling vehicle on a railway bridge has long been studied as an important design issue along with resonance of a high-speed railway bridge. Here, the VBI effect is a kind of dynamic interaction in which the vibration form of the bridge changes due to the vibration of the train when the train passes. In Japan, a design method that takes this resonance into consideration has been developed. In order to realize efficient maintenance of a huge number of existing railway bridges, which is an urgent issue in recent years, it is necessary to clarify and quantify the VBI effect again. In the monitoring of train passage waveforms, dynamic characteristics related to structural performance such as natural frequency are estimated from the response of the railway bridge when the train passes, measured by sensors, and abnormalities and damages are detected from the changes over time. The effect of deterioration or damage on railway bridges on the natural frequency is often small, and considerable accuracy is required for estimating dynamic characteristics based on train passage waveforms. At this time, the VBI effect can contribute to a decrease in estimation accuracy. In order to quantify the VBI effect mediated by the train passage waveform, it is necessary to estimate the apparent fluctuation of the dynamic characteristics of the railway bridge caused by VBI as an equivalent, time-varying, additional parameter. However, the VBI effect changes from moment to moment with the axle position (over time) on the railway bridge, and the presence of periodic external force of the traveling train makes the evaluation more difficult.

As a response evaluation method for systems with time changes, Wavelet transform, Time Varying --Vector Auto Regressive (hereinafter referred to as TV-VAR) model that allows time changes in the VAR coefficient of multivariate autoregressive model, and forgetfulness estimation of various models Time-frequency analysis such as (adaptive estimation) is known. As far as railway bridges are concerned when trains are running, Cantero and Karoumi and Matsuoka et al. Are trying to evaluate apparent fluctuations in bridge frequencies by applying the Wevelet transformation and TVP-VAR models to train-passing waveforms, respectively. In the identification of the bridge frequency during train running by the hierarchical Bayes estimation of the TV-VAR model, the TV-VAR model is used to evaluate the apparent decrease in the natural frequency of the bridge during train running from the measured acceleration response of the bridge. A TV-VAR model in which the VAR coefficient of No. 1 fluctuates stochastically with time (Time Varying) is formulated (see, for example, Non-Patent Document 1). In the identification of the bridge frequency during train running by the hierarchical Bayesian estimation of this TV-VAR model, the TV-VAR model is formulated and the unknown parameter estimation method is constructed in the hierarchical Bayesian method.

The conventional method for evaluating the amount of change in the natural frequency of a railway bridge is to measure the vibration waveform of the main girder of a concrete railway bridge, generate a mode waveform based on the measured vibration waveform, and use the standard mode based on this mode waveform. A waveform is generated, and the amount of change in the natural frequency of the railway bridge is evaluated using a TV-VAR model based on this standard mode waveform (see, for example, Patent Document 1). This conventional method for evaluating the amount of change in the natural frequency of a railway bridge prevents errors due to changes in amplitude when evaluating crack detection on the underside of the main girder of a concrete railway bridge using a TV-VAR model. And evaluate the cracks.

Hirohiro Matsuoka, 1 outside, "Identification of bridge frequency during train running by hierarchical Bayes estimation of TV-VAR model", JSCE Proceedings A1 (Structural and Seismic Engineering), Japan Society of Civil Engineers, 2012, Volume 68, Issue 3, p738-753

Japanese Unexamined Patent Publication No. 2016-194442

Both methods such as the response evaluation method for systems with time changes and the conventional evaluation method for the amount of change in the natural frequency of railway bridges are used to separate the VBI effect from the effect of regular excitation of traveling trains (external force characteristics). Has not reached. In particular, when the VBI effect becomes apparent at resonance, the vibration period based on the regular axle arrangement of the traveling train and the natural frequency of the railway bridge are close to each other, so it is necessary to separate them in the analysis of the VBI effect. It is essential. However, there is no analysis method of the time-variant system and its application example that explicitly considers the external force characteristics of the traveling train.

An object of the present invention is to provide a bridge mode characteristic estimation method and a mode characteristic estimation device thereof, which can accurately estimate the mode characteristics of a bridge by separating the vibration components of the moving body moving on the bridge. ..

The present invention solves the above problems by means of solutions as described below.
Although the description will be given with reference numerals corresponding to the embodiments of the present invention, the present invention is not limited to this embodiment.
As shown in FIGS. 7 to 9, the invention of claim 1 is a method for estimating the mode characteristics of a bridge for estimating the mode characteristics of the bridge (B), which is used when the moving body (T) moves on the bridge. Mode characteristic estimation step (# 130, S200) for estimating the mode characteristics of this bridge by separating the vibration component that the moving body vibrates this bridge from the vibration components of this bridge based on the displacement waveform of the bridge. It is a mode characteristic estimation method (# 100) of a bridge characterized by including.

The invention of claim 2 is the mode characteristic estimation method for a bridge according to claim 1, as shown in FIGS. 7 and 10, in the mode characteristic estimation step, the load of the moving moving body, which is a mode external force, is applied. Including the step of estimating the mode characteristics of the bridge by the hierarchical Bayesian estimation method of the time-varying autoregressive (TV-ARX) model with exogenous variables (A _{m) and allowing the parameters to change with time.} This is a characteristic method for estimating the mode characteristics of a bridge.

The invention of claim 3 is the mode characteristic estimation method for a bridge according to claim 1 or 2, as shown in FIGS. 6, 10 and 14 to 16, in the mode characteristic estimation step of the bridge. This is a method for estimating mode characteristics of a bridge, which comprises a step of estimating fluctuations in the natural frequency and / or mode attenuation ratio of the bridge.

As shown in FIGS. 5 and 7, the invention of claim 4 is a bridge mode characteristic estimation device that estimates the mode characteristic of the bridge (B), and when the moving body (T) moves on the bridge. A mode characteristic estimation unit (4d) for estimating the mode characteristics of this bridge by separating the vibration component that the moving body vibrates the bridge from the vibration components of the bridge based on the displacement waveform of the bridge is provided. It is a mode characteristic estimation device (4) of a bridge characterized by.

According to the present invention, it is possible to accurately estimate the mode characteristics of a bridge by separating the vibration components of the moving body moving on the bridge.

It is a schematic diagram of the bridge which is the object of estimation of the mode characteristic in the mode characteristic estimation system of the bridge which concerns on embodiment of this invention. It is a conceptual diagram which shows typically the influence which a train mass has on a natural frequency. It is a conceptual diagram which shows typically the influence which the crack of a girder has on the natural frequency. It is a conceptual diagram which shows typically the relationship between a train passing waveform and each influence factor. It is a block diagram of the mode characteristic estimation system of a bridge which concerns on embodiment of this invention. It is a graph which shows the application example to the measured waveform by the mode characteristic estimation apparatus of the bridge which concerns on embodiment of this invention as an example, (A) is the graph of the measured waveform of the vibration of a resonance bridge, and (B) is natural vibration. It is a graph which shows the fluctuation rate of a number. It is a schematic diagram for demonstrating the estimation principle of the mode characteristic estimation part in the mode characteristic estimation apparatus of a bridge which concerns on embodiment of this invention. It is a process drawing of the mode characteristic estimation method of a bridge which concerns on embodiment of this invention. It is a flowchart of the mode characteristic estimation method of a bridge which concerns on embodiment of this invention. It is a subroutine of the mode characteristic estimation processing in the mode characteristic estimation method of a bridge which concerns on embodiment of this invention. It is a schematic diagram which shows the axle arrangement of the vehicle of the traveling train set in the numerical experiment of the mode characteristic estimation method of the bridge which concerns on embodiment of this invention. It is a figure which shows the waveform for verification and the set correct answer value in the verification of the numerical experiment of the mode characteristic estimation method of the bridge which concerns on the Example of this invention, (A) is the created displacement waveform, (B) is the outside. It is a raw variable (mode external force), (C) is the set time-varying coefficient β ₁ , (D) is the set time-varying coefficient β ₂ , (E) is the set natural frequency, and (F) is the set natural frequency. Set mode attenuation ratio. It is a figure which shows the hierarchical Bayes estimation result of the TV-ARX model in the verification of the numerical experiment of the mode characteristic estimation method of the bridge which concerns on the Example of this invention, (A) is a displacement waveform, (B) is a natural frequency. (C) is the mode attenuation ratio, (D) is the time-varying coefficient β ₁ , and (E) is the time-varying coefficient β ₂ . It is a graph which shows the estimation result of the primary resonance waveform by the mode characteristic estimation method which concerns on embodiment of this invention as an example, (A) is the estimation result of a displacement waveform, and (B) is the estimation result of a natural frequency. Yes, (C) is the estimation result of the mode attenuation ratio. It is a graph which shows the estimation result of the secondary resonance waveform by the mode characteristic estimation method which concerns on embodiment of this invention as an example, (A) is the estimation result of a displacement waveform, and (B) is the estimation result of a natural frequency. Yes, (C) is the estimation result of the mode attenuation ratio. It is a graph which shows the estimation result of the 3rd order resonance waveform by the mode characteristic estimation method which concerns on embodiment of this invention as an example, (A) is the estimation result of a displacement waveform, and (B) is the estimation result of a natural frequency. Yes, (C) is the estimation result of the mode attenuation ratio.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
The track R shown in FIG. 1 is a passage (railroad track) on which the train T travels. The train T is a moving body that moves along the track R. The train T is a railroad vehicle such as an electric car, a diesel car, or a passenger car that runs on the bridge B. The train T shown in FIG. 1 is, for example, a railway vehicle of the Shinkansen (registered trademark) traveling at high speed. When the train T travels on the bridge B, the wheels periodically apply a load to the bridge B to vibrate the bridge B due to the regular shaft arrangement.

The bridge B is a fixed structure constructed so as to form a space below the track R. Bridge B is constructed so as to cross a hydrosphere such as a river, a valley, or a lake, or a traffic route such as a road or a railroad. Bridge B is, for example, a type of prestressed concrete structure, which is a concrete railway bridge with a structure (PRC structure) that allows cracks to occur under normal use conditions and controls the crack width by arranging deformed reinforcing bars and introducing prestressed concrete. is there. The bridge B includes a girder B ₁ and a pier B ₂ . The girder B ₁ is a structure arranged in the horizontal direction to support the track R. The girder B ₁ is a beam like a PRC girder that straddles one fulcrum and the other fulcrum with the pier B _{2 as a fulcrum.} The pier B ₂ is a structure that supports the girder B _1. The pier B ₂ is constructed with a predetermined interval in the length direction of the bridge B, and is a reinforced concrete column or the like arranged in the vertical direction.

Next, the characteristics of the train passing waveform measured when the train T passes over the bridge B will be described.
_{The natural frequency f of the digit B 1} shown in FIG. 1 is represented by the following number 1. Here, the EI shown in Equation _{1 is} the cross-sectional rigidity (flexural rigidity) of the girder B 1. L is a span length is the distance between the digit B ₁ fulcrum (span). Δm is the unit length mass of the digit B _1.

As shown in (1) to (3) below, the influence factors of the fluctuation of the dominant frequency in the train passing waveform include the influence of the train mass changing with time and the influence of cracks changing with time. ..
(1) Fluctuations in predominant frequency due to the position of the train T on the bridge B As shown in Fig. 2, when the train T is located on the bridge B, _{the apparent mass of the girder B 1} increases and the natural vibration occurs. The number f decreases. When the train T passes over the bridge B, the unit length mass Δm shown in Equation 1 increases to the bridge portion + the train portion (mb + mc), and the natural frequency f decreases. However, the size of the train T changes depending on the position of the train T. Further, since it is considered that not all the mass mc of the train _{vibrates together with the girder B 1} , the degree of the influence is considered to be smaller than the case where the mass mc of the train is directly substituted.

(2) Fluctuation of dominant frequency due to crack opening during train running based on PRC structure As shown in FIG. 3, when the effective cross-sectional area of the main girder decreases, the natural frequency f decreases. _{When the girder B 1} vibrates downward due to loading or vibration, the crack opens, the moment of inertia of area I shown in Equation 1 decreases, and the natural frequency f decreases. However, although the amount of decrease in the natural frequency f changes depending on the opening amount (height) of the crack, it is unknown how much deflection the crack opens to.

(3) Fluctuations in predominant frequency due to quasi-static deflection vibration In a forced vibration state due to a large number of trains T, the vibration frequency determined by the vehicle length and train speed is predominant. As shown in FIG. 4, there are factors influencing the deflection of the girder B _{1 and the natural frequency f when a single mass moves over the girder B 1 with cracks.} The state shown in FIGS. 2 and 3 changes depending on the vehicle position and the amplitude up and down. In addition, the quasi-static deflection vibration component determined by the vehicle length and train speed can be a major influencing factor during train passage.

The mode characteristic estimation system 1 shown in FIG. 5 is a system that estimates the mode characteristics of the bridge B. Here, the mode is the vibration mode or the vibration form of _{the girder B 1} , and the mode characteristic is the natural frequency and the mode attenuation ratio _{of the girder B 1.} The mode characteristic estimation system 1 is based on _{the change in the mode characteristics of the girder B 1} of the bridge B that occurs when the train T moves on the bridge B, based on the train passing waveform measured when the train T moves on the bridge B. To analyze. Mode characteristic estimating system 1, the input characteristics of the train T to move the bridge B is separated to assess the instantaneous change in the natural frequency and mode damping ratio of digits B _1. The mode characteristic estimation system 1 includes vibration measuring devices 2A and 2B, a communication device 3, a mode characteristic estimation device 4, and the like.

The vibration measuring devices 2A and 2B shown in FIGS. 1 and 5 are devices for measuring the vibration generated when the train T moves on the bridge B. The vibration measuring devices 2A and 2B detect the vibration of the _{girder B 1} generated when the train T moves on the bridge B. One of the vibration measuring devices 2A and 2B is selected and used. Vibration measurement device 2A, for example, a vibration detection device such as an accelerometer for detecting the vertical vibration acceleration digit B _1. Vibration measurement apparatus 2B, the non-contact vibration such as U Doppler for detecting the vertical vibration of the digit B ₁ based on the change in wavelength between the reflected laser beam reflected by the laser beam and column B ₁ is irradiated from the ground to the digit B ₁ It is a measuring device. The vibration measuring devices 2A and 2B measure the vibration of the central portion of the _{girder B 1} every time the train passes through the bridge B, for example. The vibration measuring devices 2A and 2B _{transmit the train passing waveform corresponding to the vibration of the digit B 1 to} the mode characteristic estimation device 4 as measurement data (vibration measurement signal).

The communication device 3 shown in FIG. 5 is a device that transmits measurement data from the vibration measuring devices 2A and 2B to the mode characteristic estimation device 4. In order to transmit measurement data from the transmitting unit of the vibration measuring devices 2A and 2B to the receiving unit 4a of the mode characteristic estimation device 4, the communication device 3 connects them so that they can communicate with each other, such as a telephone line or an internet line. Telecommunications line.

The mode characteristic estimation device 4 is a device that estimates the mode characteristics of the bridge B. The mode characteristic estimation device 4 estimates the dynamic interaction effect when the train passes. Here, the dynamic interaction is a phenomenon in which a plurality of vibration systems influence each other, and a phenomenon in which one vibration changes the vibration form of the other. The mode characteristic estimation device 4 displays the reception unit 4a, the measurement data storage unit 4b, the setting data storage unit 4c, the mode characteristic estimation unit 4d, the estimation data storage unit 4e, and the mode characteristic estimation program storage unit 4f. A unit 4g, a control unit 4h, and the like are provided. The mode characteristic estimation device 4 is configured by, for example, a personal computer or the like, and executes a predetermined process according to the mode characteristic estimation program.

The receiving unit 4a is a means for receiving the measurement data transmitted by the vibration measuring devices 2A and 2B. The receiving unit 4a receives the measurement data transmitted by the vibration measuring devices 2A and 2B through the communication device 3. The measurement data storage unit 4b is a means for storing the measurement data transmitted by the vibration measuring devices 2A and 2B. The measurement data storage unit 4b is, for example, a vibration measuring device 2A. It is a storage device that stores the measurement data transmitted by 2B in chronological order.

The setting data storage unit 4c is a means for storing various data necessary for estimating the mode characteristics of the bridge B. The setting data storage unit 4c has, for example, an axis arrangement (axle arrangement) which is an arrangement of axles in the length direction of the vehicle when the train T is viewed from the side, and a speed of the train T moving on the bridge B (train speed). ) v and a span length L of the digit B _1, first axle and time t from the passes through the reference position of the digit B ₁ of the train T, the parameters necessary to estimate the modal properties, the initial unknown parameters It is a storage device that stores values, prior distribution parameters, the number of times sampling is repeated, the number of times sampling is completed, and the like as setting data. Here, the shaft arrangement is, for example, as shown in FIG. 11, the distance between the axle centers of the front and rear wheels of the bogie (wheelbase) and the distance between the axles of the opposing wheels of the front and rear bogies (bogie spacing). And the data about the length of the vehicle (body length). The time t is, for example, the time at which the train T starts approaching the _{girder B 1} , and is related to the time after the first axle of the train T passes the fulcrum (reference position) on the entrance side of the _{girder B 1.} It is data.

The mode characteristic estimation unit 4d separates the vibration component that the train T vibrates the bridge B from the vibration component of the bridge B based on the displacement waveform of the bridge B when the train T moves on the bridge B, and the bridge This is a means for estimating the mode characteristics of B. The mode characteristic estimation unit 4d estimates the mode characteristic of the bridge B by the hierarchical Bayes method of the Time varying Auto regressive with exogenous (hereinafter referred to as TV-ARX) model. The mode characteristic estimation unit 4d considers the load of the train T traveling on the bridge B as a mode external force, and the train has been classified as forced vibration by the hierarchical Bayes method of the TV-ARX model that allows time change in the parameters. The VBI effect is evaluated based on the resonance waveform at the time of passing (train passing waveform). The mode characteristic estimation unit 4d extends the Time varying Auto regression (TV-AR) model, which is a time-frequency response analysis method, to the TV-ARX model that can consider the external force component, and the mode of the traveling train. The external force is introduced as an exogenous variable (external variable) to estimate the fluctuation of the natural frequency and mode attenuation ratio of the bridge B. Mode estimation unit 4d is, after separating the vibration component and a mode characteristic digit B ₁ of the train T running contained in the measured waveform, and estimates the modal properties of the digit B ₁ that varies instantaneously. _{The mode characteristic estimation unit 4d compares the mode characteristic of the digit B 1} at the time of minute amplitude with the mode characteristic of the digit B ₁ that fluctuates instantaneously, and thereby, the additional mass effect (natural frequency of the natural frequency) due to the traveling train T. The amount of decrease) and the additional damping effect (the amount of increase in the mode attenuation ratio) are evaluated.

FIG. 6 is a graph showing the analysis result of the measured waveform obtained by measuring the vibration of the resonant bridge from the ground side, and is the analysis result when the bridge length is 30 m and the train speed is 224 km / h. The vertical axis shown in FIG. 6 (A) is _{the displacement of the digit B 1} , and the horizontal axis is the time (s). The vertical axis shown in FIG. 6B is the volatility of the natural frequency, and the horizontal axis is time (s). The volatility of the natural frequency shown in FIG. 6B is the estimated natural frequency (estimated value) of _{the digit B 1 when the natural frequency of the digit B 1 at} a minute amplitude is 1. As shown in FIG. 6 (B), gradually increases the natural frequency of the digits B ₁ when the digit B ₁ train T is moved, the natural frequency of the digits B ₁ is opened cracks displaced on the lower side When the girder B ₁ is displaced upward and the crack is closed, the natural frequency is increased, and the natural frequency is increased or decreased according to the opening and closing of the crack. As shown in FIG. 6 (B), there is a tendency that the natural frequency in digits B ₁ in the train passage is decreased depending on the lower amplitude, at the most about 15% in comparison with the small amplitude after train passing It is decreasing, and it is possible to estimate the natural frequency that decreases momentarily due to the VIB effect and cracks.

Next, the principle of estimating the mode characteristics of the bridge by the mode characteristic estimation device according to the embodiment of the present invention will be described.
Mode estimation unit 4d is to become a TV-ARX model with discrete to the VBI model varying coefficient at the beta _m by the central difference at equal intervals delta, digit B ₁ by TV-ARX model shown in the equation (2) below Estimate the mode characteristics.

Here, m shown in Equation 2 is a discrete time point m = 1, ..., M at time t = (Δ-1) m. Mode estimation unit 4d, as shown in FIG. 7, and calculates the axial arrangement of the train T, the mode external force based on the span length L of the velocity v and the digit B ₁ of the train T as exogenous variables A _m. Mode estimation unit 4d reads the exogenous variables A shaft arrangement of the train T is the data necessary for the calculation of _m, setting data, such as velocity v, and the digit B ₁ span length L of the train T data storage unit 4c To calculate the mode external force. Mode estimation unit 4d, when introducing a random walk process shown in the following Equation 3 as varying coefficient beta _m, then calculating the unknown parameters of the equation 3, the variation of the natural frequency and modal damping ratios digit B ₁ To estimate.

The TV-ARX model is composed of Equations 2 and 3, and when interpreted as Bayesian modeling, it can be understood as a hierarchical Bayesian model in which the time-varying coefficient βm has a hierarchical prior distribution. Mode estimation unit 4d, using the pole λ which satisfies the characteristic equation shown in the equation (4) below, and the natural frequency f _m moment a natural frequency of the bridge B for the discrete time point m, bridges at each discrete time point m _{The instantaneous mode attenuation ratio ξ m} , which is the mode attenuation ratio of B, is estimated by the following equations 5 and 6.

_{The mode characteristic estimation unit 4d estimates the mode characteristic of the digit B 1} by the hierarchical Bayesian estimation method of the TV-AIR model using Gibbs sampling, which is one of the Markov chain Monte Carlo (hereinafter referred to as MCMC) method. Here, the MCMC method is a method of obtaining a probability density function that approximates a simultaneous posterior probability density function by numerical calculation. Mode estimation unit 4d is multiplexed in order to realize high-speed estimation taking into account the uncertainties, along with incorporating estimation process of exogenous variables A _m, with respect to estimation of varying coefficient beta _m when the calculation load greater An efficient sampling method of conditional probabilities is introduced to estimate the mode characteristics of _{digit B 1.} For example, the mode characteristic estimation unit 4d uses the independence of variance in conditional establishment to sample a Durbin and Koopman type smoother (hereinafter referred to as DK smoother), which is a sampling method with high calculation efficiency, with a time variation coefficient β _m . Introduces to and estimates the mode characteristics of _{digit B 1.} The mode characteristic estimation unit 4d sets data such as unknown parameters, initial values of unknown parameters, prior distribution parameters, sampling repeat counts, and sampling end counts, which are data necessary for calculations such as the _{time-varying coefficient β m.} It is read from the data storage unit 4c and the time variation coefficient β _m is calculated. Mode estimation unit 4d, and outputs the estimated data storage unit 4e instantaneous natural frequency f _m and the instantaneous mode damping ratio xi] _m bridge B after it estimated as an estimated data (mode characteristic signal).

The estimation data storage unit 4e shown in FIG. 5 is a means for storing the estimation result of the mode characteristic estimation unit 4d. The estimation data storage unit 4e is a storage device that stores the estimation data output by the mode characteristic estimation unit 4d in chronological order.

The mode characteristic estimation program storage unit 4f is a means for storing a mode characteristic estimation program for estimating the mode characteristics of the bridge B. The mode characteristic estimation program storage unit 4f is a storage device that stores a mode characteristic estimation program read from an information recording medium or a mode characteristic estimation program captured through a telecommunication line.

The display unit 4g is a means for displaying various information about the mode characteristic estimation device 4. The display unit 4g displays on the screen the fluctuation rate of the natural frequency when the train passes as shown in FIG. The display unit 4g is a display device that displays, for example, the measurement results of the vibration measuring devices 2A and 2B and the estimation results of the mode characteristic estimation unit 4d on the screen.

The control unit 4h is a central processing unit (CPU) that controls various operations related to the mode characteristic estimation device 4. The control unit 4h reads the mode characteristic estimation program from the mode characteristic estimation program storage unit 4f, and executes the mode characteristic estimation process according to the mode characteristic estimation program. For example, the control unit 4h outputs the measurement data output by the reception unit 4a to the measurement data storage unit 4b, commands the measurement data storage unit 4b to store the measurement data, and receives the measurement data from the measurement data storage unit 4b. Read and output to the mode characteristic estimation unit 4d, read the setting data from the setting data storage unit 4c and output it to the mode characteristic estimation unit 4d, or command the mode characteristic estimation unit 4d to estimate the mode characteristics of the bridge B. , The estimation data output by the mode characteristic estimation unit 4d is output to the estimation data storage unit 4e, the storage of the estimation data is commanded to the estimation data storage unit 4e, and the measurement is performed from the measurement data storage unit 4b and the estimation data storage unit 4e. The data and the estimated data are read out and output to the display unit 4g, and the display of the measurement data and the estimated data is instructed to the display unit 4g. In the control unit 4h, the receiving unit 4a, the measurement data storage unit 4b, the setting data storage unit 4c, the mode characteristic estimation unit 4d, the estimation data storage unit 4e, the mode characteristic estimation program storage unit 4f, and the display unit 4g can communicate with each other. It is connected.

Next, a method for estimating the mode characteristics of the bridge according to the embodiment of the present invention will be described.
The mode characteristic estimation method # 100 shown in FIG. 8 is a method of estimating the mode characteristic of the bridge B. In the mode characteristic estimation method # 100, the dynamic interaction effect when the train passes is estimated. The mode characteristic estimation method # 100 includes a resonance bridge detection step # 110, a vibration measurement step # 120, a mode characteristic estimation step # 130, and the like.

The resonance bridge detection step # 110 is a step of detecting the resonance generated in the bridge B when the train T moves on the bridge B. In the resonance bridge detection step # 110, for example, the vertical accelerations of the leading car and the trailing car of the train T moving on the bridge B are measured, and the amplification coefficient is calculated based on the vertical acceleration waveforms of the leading car and the trailing car. A resonant bridge is detected by comparing this impact coefficient with the bridge impact coefficient.

The vibration measurement step # 120 is a step of measuring the vibration generated when the train T moves on the bridge B. _{In the vibration measurement step # 120, the vibration of the girder B 1} generated when the train T moves on the bridge B detected as the resonance bridge in the resonance bridge detection step # 110 is measured by the vibration measuring devices 2A and 2B shown in FIG. To do.

In the mode characteristic estimation step # 130, the vibration component that the train T vibrates the bridge B is separated from the vibration component of the bridge B based on the displacement waveform of the bridge B when the train T moves on the bridge B. This is a step of estimating the mode characteristics of the bridge B. In the mode characteristic estimation step # 130, fluctuations in the natural frequency and mode attenuation ratio of the bridge B are estimated by the hierarchical Bayes method of the TV-ARX model.

In step 100 (hereinafter referred to as S) shown in FIG. 9, the control unit 4h reads the mode characteristic estimation program from the mode characteristic estimation program storage unit 4f. When the control unit 4h reads the mode characteristic estimation program, the control unit 4h starts a series of processes.

In S200, the control unit 4h commands the mode characteristic estimation unit 4d to estimate the mode characteristics of the bridge B. The control unit 4h reads the measurement data from the measurement data storage unit 4b, the control unit 4h outputs the measurement data to the mode characteristic estimation unit 4d, and the control unit 4h reads the setting data from the setting data storage unit 4c. The control unit 4h outputs this setting data to the mode characteristic estimation unit 4d. When the control unit 4h commands the mode characteristic estimation unit 4d to estimate the mode characteristics of the bridge B, the mode characteristic estimation unit 4d executes the mode characteristic estimation process.

In S300, the control unit 4h commands the display unit 4g to display the estimation result. As a result, the display unit 4g displays the fluctuation rate of the natural frequency when the train passes as shown in FIG. 6 on the screen.

Next, the mode characteristic estimation process of the bridge according to the embodiment of the present invention will be described.
In S201 shown in FIG. 10, the exogenous variable A _m-mode estimation unit 4d is computed. The mode characteristic estimation unit 4d executes the Gibbs sampling calculation procedure incorporating the DK smoother. Here, in FIG. 10, the number of samplings is shown on the right shoulder of each variable. The mode characteristic estimation unit 4d calculates the _{mode external forces A i and t} from the train speed of the target train passing waveform and the start of approach by the following equation 7.

Here, the mode external forces A _{i and t} shown in Equation 7 are synonymous with the exogenous variables A _m , v is the speed of the train T, L is the span length of _{the girder B 1 of the bridge B, and τ i} is. In a train T having a total of nw _{axles, the distance from the end of the girder B 1} at the initial time to the i-th (i = 1, ..., Nw) axle, and t is the first axle of the train T being the girder B ₁ It is the time after passing the reference position ( _{the fulcrum on the entrance side of the girder B 1} ), and H is a snake site unit function. In S201, the initial value of the unknown parameter shown in FIG. 10, the parameter of the prior distribution, the number of repetitions (burn-in) until the sampling converges to the stationary process, the number of completions of sampling, and the like are set. Here, the initial value of the unknown parameter can substitute the estimation result of the normal ARX model. For example, the initial value of the unknown parameter, the parameter of the prior distribution, the number of times of repeating sampling, the number of times of sampling end, etc. are preset and stored in the setting data storage unit 4c as setting data, and this setting data is stored in the setting data storage unit 4c. The mode characteristic estimation unit 4d reads from the unit 4c.

In S202, the mode characteristic estimation unit 4d randomly generates a _{prior distribution parameter β 1} ^{(n) at the number of samplings n.} The mode characteristic estimation unit 4d generates a random number of the prior distribution parameter β ₁ ^{(n) by the following equation 8.}

In S203, the mode characteristic estimation unit 4d generates a random number of the parameter B ^{(n) at the number of sampling times n.} The mode characteristic estimation unit 4d generates random numbers for parameter B ⁽ⁿ⁾ by the DK smoother shown in Equation 9 below.

In S204, the mode characteristic estimation unit 4d calculates ^{the parameter α (n) of the number of samplings n.} The mode characteristic estimation unit 4d calculates the parameter α ^{(n) according to the following equation tens.}

In S205, the mode characteristic estimation unit 4d randomly generates a _{parameter σ ε} ^{(n) at the number of samplings n.} The mode characteristic estimation unit 4d generates a random number of the parameter σ _ε ^{(n) according to the following equation 11.}

In S206, the mode characteristic estimation unit 4d randomly generates _{a parameter Σ v} ^{(n) of the number of samplings n.} The mode characteristic estimation unit 4d generates a random number of the parameter Σ _v ^{(n) according to the following equation 12.}

In S207, the mode characteristic estimation unit 4d determines whether or not the number of sampling ends is larger than the number of repeated samplings that is sufficiently large. When the mode characteristic estimation unit 4d determines that the number of sampling ends is larger than the number of sampling repetitions, the process proceeds to S208. When the mode characteristic estimation unit 4d determines that the number of times the sampling is repeated and the number of times the sampling is completed are the same, the process proceeds to S209. When the mode characteristic estimation unit 4d determines that the number of sampling ends is smaller than the number of sampling repetitions, the process proceeds to S210.

In S208, the ^{mode characteristic estimation unit 4d records the unknown parameter θ (n)} = [B ⁽ⁿ⁾ , σ _ε ⁽ⁿ⁾ , Σ _v ⁽ⁿ⁾ , α ⁽ⁿ⁾ ] in the setting data storage unit 4c. If the parameter theta ⁽ⁿ⁾ of the mode estimation unit 4d is output to the control section 4h, the parameter theta ⁽ⁿ⁾ of the control unit 4h outputs the setting data storage unit 4c, the setting data storage unit 4c parameter theta ⁽ⁿ⁾ Store as setting data.

In S209, the time-series mode estimation unit 4d of the instantaneous estimates of the natural frequency f _m and the instantaneous mode damping ratio xi] _m is calculated. The mode characteristic estimation unit 4d calculates the expected value of the time-varying coefficient β _m ⁽ⁿ⁾ for each discrete time point m, and the mode characteristic estimation unit 4d calculates the estimated value of _{the time-varying coefficient β m.} time series mode estimation unit 4d of the instantaneous estimates of the natural frequency f _m and the instantaneous mode damping ratio xi] _m by substituting the is computed.

In S210, the mode characteristic estimation unit 4d sets the number of sampling ends to n = n + 1. The mode characteristic estimation unit 4d increments the number of sampling ends and returns to S202, and the mode characteristic estimation unit 4d repeats the processing after S202.

The bridge mode characteristic estimation method and the mode characteristic estimation device according to the embodiment of the present invention have the following effects.
(1) In this embodiment, the vibration component that the train T vibrates the bridge B is separated from the vibration component of the bridge B based on the displacement waveform of the bridge B when the train T moves on the bridge B. Estimate the mode characteristics of bridge B. For this reason, we have constructed a highly accurate mode characteristic identification method that separates the apparent fluctuations due to the VBI effect when the vibration period of the traveling train and the natural frequency of the bridge B are close to each other and the VBI effect becomes apparent. can do.

(2) In this embodiment, the load of the train T to move a mode external force and exogenous variables A _m, a hierarchical Bayesian estimation of varying autoregressive model time exogenous with variables allow time variation of the parameters, bridges Estimate the mode characteristics of B. Therefore, it is possible to construct a TV-ARX and its hierarchical Bayesian estimation method in which the train load is considered as an exogenous variable as the mode external force and the temporal fluctuation of the parameter is considered. As a result, Bayesian time-frequency analysis of the dynamic interaction effect with the train T generated in the resonant railway bridge can be performed, and the VBI effect can be evaluated based on the displacement response of the railway bridge when the train passes. For example, it is possible to identify the instantaneous natural frequency f _m and the instantaneous mode damping ratio xi] _m varies temporally by VBI effect from the forced vibration state when the train passes.

(3) In this embodiment, the fluctuation of the natural frequency and / or the mode attenuation ratio of the bridge B is estimated. Therefore, the VBI effect caused by the interaction of the bridge B with the vehicle when the train passes can be estimated as the time variation of the natural frequency and the mode attenuation ratio. As a result, the amount of decrease in rigidity of the extracted low-rigidity resonance bridge can be quantitatively evaluated from the ground. For example, it is possible to estimate the decrease in the natural frequency of digits B ₁ by opening the crack based on the measured deflection waveform digit B _1. Further, it is possible to evaluate the rigidity reduction amount due to opening of the cracking digit B ₁ when a train passes easily. For example, the deflection of the resonance bridge can be measured on-site, and the amount of decrease in rigidity can be easily confirmed on the spot. For example, the deflection waveform of the bridge B can be measured periodically from the ground side, and the health monitoring of the bridge B can be performed with high accuracy.

(Numerical experiment)
Next, verification by numerical experiments of the mode characteristic estimation method of the bridge according to the embodiment of the present invention will be described.
(Creation of input waveform by TV-ARX model)
Numerical experiments were conducted to verify the validity of the hierarchical Bayesian estimation method for the TV-ARX model. In the numerical experiment, verification corresponding to the first V (Verification) of so-called V & V (Verification and Validation) was carried out. As shown in FIG. 12, first, set the varying coefficient beta _m when calculated back from these instantaneous assuming any variation natural frequency f _m and the instantaneous mode damping ratio xi] _m as the correct value. The bridge displacement response is simulated by the TV-ARX model with no error term given as the exogenous variable A _{m and the mode external force ΣA i, t} assuming the train passing of the 8-car train with the back-calculated time variation coefficient β _m. Calculated. The resulting bridge displacement response and mode external force .SIGMA.A _i, a _t, TV-ARX an input waveform and exogenous variables A _m to hierarchical Bayesian estimation model, again by the hierarchical Bayes estimation, time-varying coefficient beta _m, the instantaneous natural oscillation The estimation accuracy was verified by estimating the number f _m and the instantaneous mode attenuation ratio ξ _m and comparing them with the correct values.

In the numerical experiment, a bridge with a span length of 25 m, a natural frequency of 2.7 Hz, a mode attenuation ratio of 0.002, and a unit length of 22 t / m was assumed as a railway bridge. The train speed was set to 230 km / h, which is close to the resonance speed, and the running train was set to an 8-car train with a body length of 25 m. As shown in FIG. 11, the axles are arranged so that the distance between the axle centers of the front and rear wheels of the bogie (wheelbase) is 2.5 m, and the distance between the axles of the opposing wheels of the front and rear bogies (wheelbase) is 15.0 m. The distance between the rotation centers of the front and rear bogies (distance between the bogie centers) is 17.5 m. The instantaneous natural frequency f _m was set to decrease by 5% as each axle passed, and the instantaneous mode attenuation ratio ξ _m was set to increase by 20% as each axle passed.

(Estimation result)
The number of times the sampling was repeated until the sampling converged to the stationary process was 2000 times, the number of times the sampling was completed was 5000 times, and the initial values were the estimated values of the ARX model, and the TV-ARX model was estimated by Hierarchical Bayesian inference. As a result, as shown in FIG. 13, time-varying coefficient beta ₁ to match the entered displacement waveform, beta ₂ are estimated accurately, resulting in instantaneous also the natural frequency f _m and the instantaneous mode damping ratio xi] _m It was confirmed that it is possible to estimate with high accuracy including the fluctuation. Therefore, that this Hierarchical Bayesian estimation of TV-ARX model according to the embodiment, it is possible to evaluate the variation of the instantaneous natural frequency f _m and the instantaneous mode damping ratio xi] _m resonance bridge under external force action which simulates a train passing Was confirmed. The above was confirmed by numerical experiments that the variation of the moment of time of train passage can not be estimated natural frequency f _m and the instantaneous mode damping ratio xi] _m can be evaluated with high accuracy in an existing time-frequency analysis method TV-VAR model.

(Evaluation of the effect of noise and time synchronization)
Random noise according to a normal distribution was added to the created displacement waveform shown in FIG. 12 (A), and hierarchical Bayesian estimation of the TV-ARX model was performed. Random numbers were generated from the standard normal distribution with the standard deviations of 1%, 2%, and 5% of the average amplitude during train passage as noise, and added to the displacement waveform. The number of times the sampling was repeated was 2000 times, the number of times the sampling was completed was 5000 times, the estimated value of the ARX model was used as the initial value, and the average error AE was used as the evaluation index. As a result, it was confirmed that the instantaneous natural frequency f _m can be estimated relatively robustly with respect to the observed noise, with an average error of about 5% even if the impossible noise is about 5%. Incidentally, even if the additive noise was present 5 percent, when compared with methods according to the existing TV-VAR model, hierarchical Bayesian estimation instantaneous natural frequency f _m and the instantaneous mode attenuation of TV-ARX model according to this embodiment It was confirmed that the ratio ξ _m can be estimated with high accuracy.

In application to actual structures, when dealing with exogenous variables (mode force) A _m shown in FIG. 12 (B) as known input, it is necessary to accurately grasp the train speed and the train enters timing. However, reality is not large when the measurement system to accurately grasp the train enters timing is established, time synchronization error occurs in the exogenous variables A _m to be input. In order to evaluate the effect of this error on the estimation result, the estimation was performed by shifting the input time of the mode external force. As the synchronization error, ± 0.01s, ± 0.02s and ± 0.04s corresponding to 0.5, 1 and 2 sampling of the observation data sampled at 50Hz were examined. Effect of time synchronization error occurs primarily at the moment the mode damping ratio xi] _m, larger tendency was confirmed when entered earlier than particular fact exogenous variables A _m. In addition, a tendency to increase rapidly was confirmed when it exceeded ± 0.02. Therefore, when it is desired to accurately estimate the instantaneous mode attenuation ratio ξ _m , time synchronization of about ± 0.01 s is required. From the above, when the sampling frequency of the measured waveform is 50 Hz, if the time synchronization error is corrected by cross-correlation etc., the time synchronization error will be at least within ± 0.01 s, and it can be applied without special time synchronization processing such as interpolation and resampling. It is considered possible. It was confirmed that the instantaneous natural frequency f _m can be estimated with a certain accuracy even if the time synchronization is slightly out of sync.

(Application to actual measured waveforms of bridges)
Next, the application of the mode characteristic estimation method of the bridge according to the embodiment of the present invention to the measured resonance waveform of the actual bridge will be described.
The measurement displacement waveform of the resonance bridges VBI effect becomes remarkable, TV-ARX applying the hierarchical Bayesian estimation model was estimated instantaneous natural frequency f _m and the instantaneous mode damping ratio xi] _m. Similarly, the hierarchical Bayesian estimation of the TV-ARX model is applied to the displacement waveform obtained by the VBI model that combines the measurement conditions and specifications for vehicles and bridges, and the VBI model exerts additional mass effect and additional damping effect. We also verified how accurately it can be calculated.

By applying the hierarchical Bayesian estimation of the TV-ARX model to the measured waveform, we verified the applicability under actual measurement conditions such as noise and time synchronization, and examined the VBI effect in an actual resonant bridge. From the measured waveforms accumulated so far, the target bridge has a resonance phenomenon when the train passes, and the span length where the first to third resonance occurred at the test running speed up to about 260 km / h is 9 to. A bridge of about 60m was selected. The measured natural frequency and the measured mode attenuation ratio were identified from the measured waveform.

(Applicable condition)
Prior to applying the hierarchical Bayesian estimation of the TV-ARX model, the time synchronization by the cross-correlation function and the mode external force term ΣA _{i, t} were set. The shaft arrangement of the vehicle is as shown in FIG. 11 for all vehicle types. Since the error between the train speed and the train approach position has a large effect on the estimation result, the train speed is in the range of ± 3 km / h and the approach position is in the range of ± 0.3 s in 0.1 km / h increments. , The train speed and approach position were estimated accurately by grid search in increments of 0.01s. Hierarchical Bayesian estimation of the TV-ARX model was performed with the number of repeated samplings being 1000 and the number of samplings after convergence being 2000. The hierarchical Bayesian estimation of the TV-ARX model was applied to the displacement waveform obtained by the VBI model that reproduced the measured waveform in the same way as the measured displacement waveform. By comparing the results of both, the accuracy of the VBI effect that occurs in the displacement waveform obtained by the VBI model was verified. The initial values and the number of samplings in the Hierarchical Bayesian estimation were the same as the measured waveforms.

(Results of application to primary resonance waveform and accuracy of VBI model)
The graph shown in FIG. 14 is a graph showing the application result to the first-order resonance waveform as an example. As shown in FIG. 14A, a resonance phenomenon in which the amplitude increases as the train passes can be confirmed in the input waveform. The thin lines (Free Vibration) shown in FIGS. 14 (B) and 14 (C) are changes in the natural frequency and mode damping ratio of the bridge alone identified by considering the waveform after passing the train as free vibration. The thick line (Exp.-TVARX) is the change in the natural frequency and mode attenuation ratio when the hierarchical Bayesian estimation of the TV-ARX model is applied to the measured waveform. The dotted line (VBI-TVARX) is the change in the natural frequency and mode attenuation ratio when the hierarchical Bayesian estimation of the TV-ARX model is applied to the displacement waveform calculated by the VBI model that reproduces the measured waveform. The thick and dotted lines shown in FIGS. 14B and 14C are the instantaneous natural frequency f _m and the instantaneous mode attenuation ratio ξ _{m calculated from the time variation coefficient β m} . It can be confirmed that the estimation result of the actually measured waveform shown by the thick line in FIGS. 14 (B) and 14 (C) fluctuates when the mode external force is applied. As shown in FIGS. 14B and 14C, the instantaneous natural frequency f _m tends to decrease and the instantaneous mode attenuation ratio ξ _m tends to increase as the train passes. As shown in FIG. 14 (B) (C), the instantaneous natural frequency f _m be decreased by about 0.05Hz during the train pass, moment mode damping ratio xi] _m was confirmed to be elevated approximately 1%. Instantaneous natural frequency f _m and the instantaneous mode damping ratio xi] _m indicates the same trend in the measured and VBI model. Therefore, it includes the same VBI effects and the actual bridges the bridge displacement response obtained by VBI model (decrease and increase of the instantaneous mode damping ratio xi] _m of instantaneous natural frequency f _m) was confirmed.

(Results of application to 2nd and 3rd order resonance waveforms and accuracy of VBI model)
The graph shown in FIG. 15 is a graph showing the application result to the second-order resonance waveform as an example. The graph shown in FIG. 16 is a graph showing the application result to the third-order resonance waveform as an example. The second-order resonance occurs when two waves of natural vibration of the bridge are generated, and the third-order resonance occurs when one vehicle passes at the same timing when three waves are generated. As shown in FIG. 15 (B) (C), although a slight increase or decrease the moment to the natural frequency f _m and the instantaneous mode damping ratio xi] _m in a vehicle passing timing in secondary resonance waveform can be confirmed, with the train passing It was confirmed that the instantaneous natural frequency f _m decreased and the instantaneous mode attenuation ratio ξ _{m increased.} On the other hand, as shown in FIGS. 16B and 16C, it was confirmed that _{in the third-order resonance waveform, the instantaneous natural frequency f m} decreases and the instantaneous mode attenuation ratio ξ _{m increases each time the vehicle passes on the vehicle.} Was done. It was confirmed that the adjacent lower peaks shown in FIGS. 16B and 16C correspond to the bogies of the vehicle, and the natural frequency decreases each time the bogies pass. Since the span length of the bridge having the third-order resonance waveform is 9.3 m, which is shorter than the bogie interval of 15 m, there is a time when the axle is not on even while the train is passing. Moment natural frequency f _m and the instantaneous mode damping ratio xi] _m practically at such a timing, coincides with the natural frequency and mode damping ratio of the bridge itself, is VBI effect if there is no axle on bridge It was confirmed that it could not be obtained. In addition, it was confirmed that the VBI effect obtained by the VBI model for both the second-order resonance and the third-order resonance is in good agreement with the application results for actual measurement. In this way, it is demonstrated that the apparent fluctuation of the natural frequency and mode attenuation ratio due to the VBI effect can be estimated from the measured displacement waveform by the hierarchical Bayesian estimation of the TV-ARX model, and the bridge displacement waveform obtained by the VBI model. It was clarified that the same VBI effect as the actual measurement is included in.

From the above, it was demonstrated that the VBI effect occurs not only in the first-order resonance but also in the second-order and third-order resonances. In addition, the hierarchical Bayesian estimation of the TV-ARX model is applied to the resonance waveform calculated by the VBI model under the same conditions as the actual bridge, and the natural frequency and mode attenuation estimated by the hierarchical Bayesian estimation of the TV-ARX model from the measured resonance waveform. Compared to the ratio. As a result, the temporal fluctuations of both were almost the same, and the validity of the VBI effect obtained by the VBI model could be shown at the waveform level for the first time. In addition, by applying the hierarchical Bayesian estimation of the TV-ARX model to the measured resonance waveform and the resonance waveform obtained by analyzing the VBI model, the VBI effect that occurs in the train passing waveform can be demonstrated, and the VBI model can be used. We were able to verify the validity of the VBI effect. Furthermore, the demonstration of the VBI effect at the waveform level based on the measured waveform and the verification of the analysis accuracy of the VBI effect became possible for the first time by the hierarchical Bayesian estimation of the TV-ARX model.

The present invention is not limited to the embodiments described above, and various modifications or modifications can be made as described below, and these are also within the scope of the present invention.
(1) In this embodiment, the case where the bridge B is a concrete bridge provided with a PRC girder has been described as an example, but the present invention can also be applied to the case where the bridge B is a steel bridge. Further, in this embodiment, the case where the moving body is a railroad vehicle has been described as an example, but the present invention can also be applied to the case where the moving body is a magnetic levitation type railroad vehicle. Further, in this embodiment, the case where the train T is a Shinkansen vehicle traveling on the Shinkansen has been described as an example, but the conventional line vehicle traveling on the conventional line or the Shinkansen and the conventional line mutually travel. The present invention can also be applied to possible vehicles for direct driving.

(2) In this embodiment, the vibration measurement device 2A, but 2B has been described an example in which an acceleration sensor or U Doppler, based on the expansion and contraction of the piano wire connecting the digit B ₁ and the ground of the bridge B The present invention can also be applied to a ring-type displacement meter that measures displacement due to vibration. Further, in this embodiment, the case where the mode characteristic estimation unit 4d estimates the fluctuations of both the natural frequency and the mode attenuation ratio has been described as an example, but the fluctuation of one of the natural frequency or the mode attenuation ratio has been described. The present invention can also be applied to the case where the mode characteristic estimation unit 4d estimates.

(3) In this embodiment, a case where a random walk process is introduced and the fluctuation of the natural frequency and the mode attenuation ratio is estimated by the mode characteristic estimation unit 4d has been described as an example. It does not limit the invention. For example, the present invention can be applied to the case where the estimation parameter is reduced by introducing a functional form based on the mode external force to the temporal change of the natural frequency and the mode attenuation ratio in the estimation of the VBI effect. .. Further, in this embodiment, the case where the mode characteristic of the bridge B is estimated by using the displacement waveform of the bridge B as the measured waveform has been described as an example. However, the measured waveform created by the VBI model that reproduces the measured waveform is used as the measured waveform of the bridge B. The present invention can also be applied to the case where the mode characteristic of the bridge B is estimated as the displacement waveform.

1 Mode characteristic estimation system 2A, 2B Vibration measuring device 3 Communication device 4 Mode characteristic estimation device 4d Mode characteristic estimation unit 4h Control unit R Track B Bridge B ₁ digit T Train (moving body)
A _m exogenous variable β _m time variation coefficient f _m instantaneous natural frequency ξ _m instantaneous mode attenuation ratio

Claims (4)

It is a method of estimating the mode characteristics of a bridge, which estimates the mode characteristics of a bridge.
Based on the displacement waveform of this bridge when the moving body moves on the bridge, the vibration component that the moving body vibrates this bridge is separated from the vibration component of this bridge, and the mode characteristic of this bridge is estimated. Including the mode characteristic estimation process,
A method for estimating the mode characteristics of a bridge. In the method for estimating the mode characteristics of a bridge according to claim 1,
In the mode characteristic estimation step, the load of the moving body, which is a mode external force, is used as an exogenous variable, and the bridge is subjected to a hierarchical Bayesian estimation method of a time-varying autoregressive model with an exogenous variable that allows time variation of parameters. Including the step of estimating the mode characteristics,
A method for estimating the mode characteristics of a bridge. In the method for estimating the mode characteristics of a bridge according to claim 1 or 2.
The mode characteristic estimation step includes a step of estimating fluctuations in the natural frequency and / or mode attenuation ratio of the bridge.
A method for estimating the mode characteristics of a bridge. It is a mode characteristic estimation device for bridges that estimates the mode characteristics of bridges.
Based on the displacement waveform of this bridge when the moving body moves on the bridge, the vibration component that the moving body vibrates this bridge is separated from the vibration component of this bridge, and the mode characteristic of this bridge is estimated. To have a mode characteristic estimation unit
A mode characteristic estimation device for bridges.

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