JP2005069986A - Vibration predicting system for object - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a vibration predicting system for an object, capable of high-precisely predicting the waveform of the vibration of the object and the maximum amplitude thereof, even if the fluctuation of fluid is unsteady. <P>SOLUTION: Firstly, by providing time-history data on the flow velocity of the fluid, this fluctuation in the flow velocity is decomposed by discrete wavelet transformation (S102). The time-history data is stored, for example, on a disk as sampled digital data. Secondly, individual decomposed fluctuations of the flow velocity are converted into fluid forces. Here, the determined fluid forces are represented as functions of the frequency (S104). By multiplying the fluid forces expressed as functions of the frequency, by the dynamic admittance expressed as a transfer function of a subject object (S106), the vibration of the object in a decompressed state can be expressed as the function of frequency. Finally, by composing the vibrations of individual objects which are determined as the functions of the frequency, by discrete wavelet inverse transformation, the overall vibration waveform of a time function can be obtained (S108). <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to prediction of vibration of a structure / object placed in a changing fluid.

  In the conventional method for predicting the vibration of an object placed in a fluid, first, the entire fluid fluctuation waveform is converted into a frequency function by Fourier transform or the like. Only the standard deviation of the vibration of the object is obtained from the area of the function obtained by multiplying this by the fluid admittance and the mechanical admittance of the object (see, for example, Non-Patent Document 1). In this method, information about time disappears, so that the vibration waveform of the object cannot be obtained. Further, it is assumed that the fluid fluctuation is steady, and the maximum amplitude is estimated statistically to be about 3 to 3.5 times the obtained standard deviation. However, if the fluid fluctuation is non-stationary, this estimation does not hold, and therefore the maximum amplitude important for the safety of the object cannot be obtained.

Isao Okauchi, Manabu Ito, Toshio Miyata “Windproof Structure” published in Maruzen 1977 Yamada, M. and Ohkitani, K .: Orthonormal Wavelet Analysis of Turbulence, Fluid Dynamics Research, 8, pp.101-115, 1991 Meyer, Y .: Wavelets and Operators, Cambridge University Press, 1992 Daubechies, I .: Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, 1992 Fumio Sasaki, Tatsuya Maeda, Michio Yamada: Analysis of time-series data using wavelet transform, Journal of Structural Engineering, Vol. 38B, Architectural Institute of Japan pp. 9-20 1992 Davenport, A. G .: Applications of Statistical Concepts to the Wind Loading of Structures, Proceedings of Institutions of Civil Engigeers, 19, pp.449-472, 1961

  The purpose of the present invention is to predict the vibration waveform and maximum amplitude of an object with high accuracy by considering the temporal locality of the fluid fluctuation, regardless of whether the fluid fluctuation is steady or non-stationary. And providing an object vibration prediction system by a simple method.

In order to achieve the above object, the present invention is an object vibration prediction system for predicting vibration of an object in a fluid, wherein time history data of the flow velocity of the fluid is input, and a flow velocity fluctuation waveform is obtained from the time history data. Wavelet transform means for decomposing the flow rate by discrete wavelet transform, hydrodynamic force transform means for transforming individual decomposed flow velocity fluctuations into fluid forces, and from the mechanical properties of the object, the fluid force is a function of frequency. It is characterized by comprising vibration conversion means for converting to vibration and wavelet inverse conversion means for outputting a vibration waveform of a time function by means of discrete wavelet inverse transformation of the vibration of the object as a function of the frequency.
A program for causing a computer system to construct the above-described object vibration prediction system is also the present invention.

  Since the system of the present invention is simple and reflects the temporal locality of the flow, it is possible to accurately obtain the vibration waveform and maximum amplitude of the object even if the fluid fluctuation is unsteady. is there.

BEST MODE FOR CARRYING OUT THE INVENTION

EMBODIMENT OF THE INVENTION Below, the form for inventing is demonstrated using figures.
FIG. 1 is a flowchart for explaining processing in the system according to the embodiment of the present invention. 2 to 5 are diagrams for explaining each processing stage.
In FIG. 1, first, time history data relating to the flow velocity of the fluid is given, and this flow velocity fluctuation is decomposed by discrete wavelet transform (S102). The time history data is stored and stored as sampled digital data on a disk, for example. This is read and used.
As shown in FIG. 2, this process means that the original flow velocity fluctuation waveform is decomposed with discrete frequency wavelets. The original flow velocity fluctuation waveform is represented by the sum of those decomposed by discrete frequency wavelets. The discrete wavelet transform is described in, for example, the above-mentioned Non-Patent Documents 2 to 5 including the definition of the wavelet, so that detailed description thereof is omitted here.

Next, the decomposed individual flow velocity fluctuations are converted into fluid forces. The fluid force obtained here is a function of frequency (S104). As shown in FIG. 3, this is obtained by converting each decomposed flow velocity variation into a force and expressing it as a function of frequency, and multiplying it by fluid admittance.
Using the mechanical properties (mechanical admittance) of the target object, individual fluid forces are converted into vibrations of the object (S106). As shown in FIG. 4, by multiplying the fluid force expressed as a function of frequency by the mechanical admittance of the target object shown as a transfer function, the vibration of the decomposed object as a function of frequency is obtained. Can be represented.

  Finally, the vibrations of the individual objects obtained as a function of frequency are synthesized into a function of time by inverse discrete wavelet transform to obtain the entire vibration waveform (S108). As shown in FIG. 5, the vibration waveform of the object can be obtained by synthesizing the functions obtained as functions of the individual frequencies and returning them to a function of time. The vibration waveform can be output in the form of a graph, for example.

  Now, the gust response is an irregular vibration that is forcibly induced by the turbulence of the acting wind. Below, the example which applied the above-mentioned method with respect to this gust response is demonstrated in detail. An example of predicting vibration by this method is given by giving the specifications and vibration characteristics of the Akashi Kaikyo Bridge structure to the wind speed fluctuation data obtained by actual measurement. In the following description, the mainstream direction gust response of a one-degree-of-freedom system will be described.

となる。
まず、式（１）のｘ_ｊ，ｋ（ω）について述べる。風速変動ｕ（ｔ）のウェーブレット係数をａ_ｊ，ｋとすると、ａ_ｊ，ｋに対応する風速変動のフーリエ変換ｕ_ｊ，ｋ（ω）は、離散ウェーブレット基底Ψ_ｊ，ｋ（ω）を用いて、ｕ_ｊ，ｋ（ω）＝ａ_ｊ，ｋΨ_ｊ，ｋ（ω）と表される。そこで、各ｕ_ｊ，ｋ（ω）による局所的な変動抗力のフーリエ変換を従来の周波数領域におけるガスト応答解析法に習い、

と定義する。ここで、局所平均風速Ｕ_ｊ，ｋは、スケールｊおよび位置ｋの拡散ウェーブレットが支配する時間区間におけるｕ（ｔ）の平均であり、同様にＰ_ｊ，ｋは局所的な静的空気力である。また、Ｘ_Ｄ（ωｄ／（２πＵ_ｊ，ｋ））はＵ_ｊ，ｋに基づく無次元周波数を入力とする空力アドミッタンスである。ρは空気密度，ｄは代表長さ，Ｃ_Ｄは抗力係数である。 First, the response history x (t) of the response displacement to be estimated is each response x in the scale parameter j (corresponding to the frequency band) and shift parameter k (corresponding to the position on the time axis) used in the wavelet transform. _{Let j, k} (t) be a superposition and express this in the frequency domain

It becomes.
First, x _{j, k} (ω) in Expression (1) will be described. If the wavelet coefficients of the wind speed fluctuation u (t) are a _{j, k} , the Fourier transform u _{j, k} (ω) of the wind speed fluctuation corresponding to a _{j, k} uses the discrete wavelet base Ψ _{j, k} (ω). U _{j, k} (ω) = a _{j, k} Ψ _{j, k} (ω). Therefore, we learned the conventional gust response analysis method in the frequency domain for Fourier transform of local fluctuation drag by u _{j, k} (ω).

It is defined as Here, the local average wind speed U _{j, k} is the average of u (t) in the time interval dominated by the diffusion wavelet at scale j and position k, and similarly, P _{j, k} is the local static aerodynamic force. is there. X _D (ωd / (2πU _{j, k} )) is an aerodynamic admittance having a dimensionless frequency based on U _{j, k} as an input. ρ is the air density, d is the representative length, and _CD is the drag coefficient.

を得る。
式（３）と、静的成分近傍を表すη（ω）＝（１／２）ｐｄＣ_ＤＵ^２Φ_ｊ＝０（ω）／Ｋとを式（１）に代入し（Ｕ：ｕ（ｔ）全体の平均風速，Φ_ｊ＝０（ω）：スケーリング関数）、フーリエ逆変換を行えば、ガスト応答の時刻歴ｘ（ｔ）が得られる。なお、式（３）のＨ（ω）中に含まれる減衰比ζには、構造減衰ζ_０と空力減衰の和として

を用いることとする。
本手法においては、空気力が各スケールと各時刻とに依存する局所平均風速Ｕ_ｊ，ｋに基づいて計算されており、空中減衰やＸ_ＤもＵ_ｊ，ｋに応じて変化するようになっている点が特徴である。ここではＸ_Ｄを実関数とし、以下に示すDavenportの提案式（ｃのディケイファクターは１とした）（上述の非特許文献６参照）を暫定的に用いてガスト応答の推定を行う。

以上に、ガスト応答に本発明の手法を適用した場合を説明した。上述のガスト応答の推定を、実際に観測した風速変動データを用いて行った例を、図６〜図８を用いて、以下に説明する。 Multiply equation (2) by the transfer function H (ω) of the target object and divide by K

Get.
Substituting Equation (3) and η (ω) = (1/2) pdC _D U ² Φ _{j = 0} (ω) / K representing the vicinity of the static component into Equation (1) (U: u (t ) Overall average wind speed, Φ _{j = 0} (ω): scaling function), and inverse Fourier transform, the time history x (t) of the gust response can be obtained. Note that the damping ratio ζ included in H (ω) of Equation (3) is the sum of the structural damping ζ ₀ and the aerodynamic damping.

Will be used.
In this method, the aerodynamic force is calculated based on the local average wind speed U _{j, k} that depends on each scale and each time, and the air attenuation and X _D also change according to U _{j, k.} This is a feature. Here, the X _D and real function, to estimate the gust response using proposed formula Davenport shown below (decay factor c is set to 1) (Non-Patent Document 6 above) tentatively.

The case where the method of the present invention is applied to the gust response has been described above. An example in which the above-described estimation of the gust response is performed using actually observed wind speed fluctuation data will be described below with reference to FIGS.

<Application example>
FIG. 6 shows wind speed fluctuation data given to the analysis. This wind speed fluctuation data is actually measured by sampling at 20 Hz with an ultrasonic anemometer on the roof of a building in an urban area. Although 66 pieces of time history data with a measurement time of 10 minutes are obtained, for the convenience of using FFT for wavelet transform, data of about 409 seconds of each time history is targeted. The wind speed fluctuation data shown in FIG. 6 is an example of the measured wind speed fluctuation u (t) of the mainstream direction component. Slightly large fluctuations are observed in the vicinity of 170 s, and after 300 s, the fluctuations tend to decrease and the average wind speed tends to decrease. Based on the relative speed between the wind speed and the structure, a time history response analysis in which an external force is applied is performed on these actually measured data.
The specifications and vibration characteristics of the structure to be analyzed are those of Akashi Kaikyo Bridge. As the natural frequency, 0.116 Hz, which is about three times the horizontal primary mode natural frequency, is given. Also, C _D and zeta ₀ uses a result of the wind tunnel experiment.
FIG. 7 shows the response displacement x _P (t) of the Akashi Kaikyo Bridge estimated by this method for the wind speed fluctuation data of FIG. For the scale function Φ _{j = 0} (ω) and the discrete wavelet basis Ψ _{j, k} (ω) of Equation (2), a Meyer system function constructed by Yamada et al. Is used (see Non-Patent Documents 2 and 5). ). In FIG. 7, a large amplitude is generated in the vicinity of 170 s.
X _P (t) was obtained by this method for all natural winds, and the peak factor g ^r _p was calculated for each x _P (t). And g ^r _p obtained, it shows the relationship between the g ^r obtained by the numerical analysis is a FIG. The vertical axis value of g ^r obtained by numerical analysis, the horizontal axis is the value of g ^r _p estimated by this method. The vertical axis and the horizontal axis represent the maximum amplitude as a magnification with respect to the standard deviation. When g ^r is remarkably large, there is a case where g ^r _p does not coincide with this, but it is consistent as a whole, and the present method has sufficient accuracy.

It is a flowchart which shows the process in the system of embodiment of this invention. It is a figure explaining the decomposition | disassembly process by discrete wavelet transform of a flow-velocity fluctuation waveform. It is a figure explaining the process which converts each decomposed | disassembled flow velocity fluctuation | variation into fluid force. It is a figure explaining the process which converts each fluid force into the vibration of an object. It is a figure explaining the process which synthesize | combines the vibration of each object and obtains the whole vibration waveform. It is a figure which shows the example (observed wind speed) of the flow-velocity fluctuation waveform. It is a figure which shows the example of the prediction waveform of the vibration obtained by this system. It is a figure which shows the comparison with the predicted value obtained by this system, and the value obtained by numerical analysis.

Claims (2)

An object vibration prediction system for predicting vibration of an object in a fluid,
Wavelet transform means for inputting the time history data of the flow velocity of the fluid and decomposing the flow velocity fluctuation waveform from the time history data by discrete wavelet transform;
A fluid force converting means for converting individual decomposed flow velocity fluctuations into fluid forces;
From the mechanical properties of the object, vibration converting means for converting the fluid force into vibration of the object that is a function of frequency;
An object vibration prediction system, comprising: wavelet inverse transform means for outputting a vibration waveform of a time function by performing discrete wavelet inverse transform on the vibration of the object as a function of the frequency. A program causing a computer system to construct the object vibration prediction system according to claim 1.

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