WO2010021336A1 - Dispositif d'analyse d'oscillation et procédé d'analyse d'oscillation - Google Patents

Dispositif d'analyse d'oscillation et procédé d'analyse d'oscillation Download PDF

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WO2010021336A1
WO2010021336A1 PCT/JP2009/064496 JP2009064496W WO2010021336A1 WO 2010021336 A1 WO2010021336 A1 WO 2010021336A1 JP 2009064496 W JP2009064496 W JP 2009064496W WO 2010021336 A1 WO2010021336 A1 WO 2010021336A1
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vibration
data
analysis
frequency
shows
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PCT/JP2009/064496
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English (en)
Japanese (ja)
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公彦 中野
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国立大学法人東京大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H1/00—Measuring characteristics of vibrations in solids by using direct conduction to the detector
    • G01H1/003—Measuring characteristics of vibrations in solids by using direct conduction to the detector of rotating machines
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02—Preprocessing
    • G06F2218/04—Denoising
    • G06F2218/06—Denoising by applying a scale-space analysis, e.g. using wavelet analysis

Definitions

  • the present invention relates to a vibration analysis apparatus and a vibration analysis method. More particularly, the present invention relates to a technique for analyzing vibration characteristics.
  • Non-Patent Document 3 mode analysis has been proposed as a mechanical vibration analysis method (Non-Patent Document 3 below). According to this, the frequency of vibration and spatial distribution (displacement) can be obtained. However, it is still difficult to know the time change of vibration.
  • PARAFAC also called multi-layer factor analysis
  • This method originates from the measurement method used in psychology and has begun to be used in the field of chemical analysis such as spectrum analysis of fluorescein (fluorescein).
  • fluorescein fluorescein
  • attempts have been made to apply it to electroencephalogram analysis. By combining with complex wavelet transform, it is possible to investigate temporal changes and spatial distribution of electroencephalograms divided into ⁇ , ⁇ , ⁇ bands, etc. Patent Document 2).
  • a main object of the present invention is to provide an apparatus and a method capable of acquiring characteristics related to a temporal change of vibration.
  • the present invention has a configuration described in any of the following items.
  • the vibration acquisition unit is configured to acquire vibration data at a plurality of locations
  • the frequency analysis unit is configured to generate multidimensional vector data that is a function of time and frequency by analyzing the vibration data
  • the multi-layer factor analysis unit is configured to generate a plurality of independent vectors using the multidimensional vector data.
  • At least one of the plurality of vectors generated by the multilayer factor analysis unit represents the temporal characteristics of vibration.
  • the vibration to be analyzed is, for example, mechanical vibration.
  • the vibration may be a vibration of sound or electromagnetic waves in addition to the mechanical vibration.
  • Vibration analysis method comprising the following steps (1) obtaining vibration data at a plurality of locations; (2) generating multidimensional vector data that is a function of time and frequency by analyzing the vibration data; (3) A step of generating a plurality of independent vectors using the multidimensional vector data.
  • This computer program can be recorded on various recording media such as a magnetic recording medium (such as a hard disk), an electrical recording medium (such as a flash memory or DRAM), an optical recording medium (such as a CD or DVD), or a magneto-optical recording medium (such as a hard disk). MO etc.).
  • the type of the recording medium is not limited to these.
  • the program can be transmitted as a signal via various media (such as an optical fiber and a copper wire).
  • This program can be written in various languages (for example, C language or assembly language).
  • the program may be described in a language that requires compilation before execution. In this case, the program may be a pre-compiled program or a compiled program.
  • the vibration analysis apparatus includes a vibration acquisition unit 1, a frequency analysis unit 2, and a multilayer factor analysis unit 3.
  • the vibration acquisition unit 1 is configured to acquire vibration data at a plurality of locations.
  • the vibration data is acceleration data at a certain point, for example.
  • vibration data in addition to acceleration, data of an image taken by a speed, displacement, and high-speed camera can be used.
  • a so-called accelerometer can be used to acquire acceleration data.
  • the frequency analysis unit 2 is configured to generate multidimensional vector data that is a function of time and frequency by analyzing the vibration data acquired by the vibration acquisition unit 1. Specifically, in this embodiment, multidimensional vector data is generated by performing complex wavelet transform on vibration data.
  • the multilayer factor analysis unit 3 is configured to generate a plurality of independent vectors using the multidimensional vector data generated by the frequency analysis unit 2.
  • at least one of the plurality of vectors generated by the multilayer factor analysis unit 3 represents a temporal characteristic of vibration.
  • vibration analysis method Next, a vibration analysis method using the apparatus of the present invention will be described with reference mainly to the flowchart shown in FIG. Note that the vibration analysis in this embodiment is performed as a simulation. In this embodiment, a vibration analysis when vibration is applied to a simple support beam will be described as an example.
  • the beam 100 is a so-called simple support beam.
  • the beam 100 is provided with five accelerometers 11 to 15 that can ignore mass (see FIG. 3). These accelerometers 11 to 15 constitute the vibration acquisition unit 1 of the present embodiment.
  • the position of the point load is defined as l f with the left end in FIG. 3 as a reference.
  • the installation position p 1 of the accelerometers 11 ⁇ 15, p 2, p 3, p 4, p 5 , to the length l b of the beam is 10, 20, 30, 40, 50% Yes. Further, in this example, it has a length l b of the beam and 1 m.
  • the applied point load causes deflection acceleration at each point according to the distance from the left end.
  • the transfer function between the point load and the acceleration at this time is as shown in Equation (1), where s is the Laplace operator and ⁇ n is the natural angular frequency of the n-th mode.
  • k n is determined by the following equation.
  • the numerical values of the beams are shown in Table 1 below.
  • the primary, secondary and tertiary natural frequencies of this beam are 145.9 rad / s (23.2 Hz), 583.4 rad / s (92.9 Hz) and 1312.7 rad / s (208.9 Hz), respectively.
  • the vibration applied to the beam in this way is acquired by each accelerometer 11 to 15 and sent to the frequency analysis unit 2.
  • the frequency analysis unit 2 performs frequency analysis as follows.
  • wavelet transform is used as frequency analysis.
  • wavelet transform is performed on the time history data regarding acceleration at each point acquired by the accelerometers 11 to 15.
  • Wavelet transform can convert one-dimensional time history data into “two-dimensional data with frequency and time axes”. If the acceleration data at each point is s (t), the wavelet transform is defined as follows. Here, a is the scale and b is the position.
  • ⁇ (t) represents a mother wavelet.
  • Various mother wavelets have been proposed.
  • a complex Morlet is used.
  • Complex Morlet has a feature that it is easy to define a frequency and is composed of sine and cosine waves, and is represented by the following equation (4).
  • f b is a bandwidth parameter
  • f c is a center frequency.
  • the scale a is converted to a frequency f (Hz) by the following equation (5).
  • a complex multidimensional data matrix S (N f x N t x N p ) of frequency f, time t, and space p (corresponding to an example of the “multidimensional data matrix” in the present invention) can be obtained ( Step SA-3).
  • Non-Patent Document 2 the absolute value of a complex multidimensional data matrix is often the object of analysis.
  • the PARAFAC analysis is performed for each of the real part and the imaginary part. If phase information is unnecessary, the temporal characteristics of vibration can be analyzed by performing PARAFAC analysis on either the real part or the imaginary part (see the calculation example described later).
  • the generated multidimensional vector data is sent to the multilayer factor analysis unit 3.
  • the multilayer factor analysis unit 3 performs multilayer factor analysis (so-called PARAFAC analysis) on the multidimensional vector data.
  • PARAFAC analysis A schematic image of PARAFAC analysis is shown in FIG.
  • the elements of the multidimensional data matrix S (N f x N t x N p ) are S ftp, and independent three elements having a fk , b tk , and c pk as elements represented by the following expressions:
  • k represents a factor
  • N k represents the number of factors.
  • a general multidimensional data matrix cannot always be decomposed into a vector such as Equation (6). If the element of the data matrix to be obtained is S hat pft , a fk , b tk , and c pk are obtained by the alternating least squares method so as to minimize the following residual ⁇ .
  • the process of separating a multidimensional data matrix into a number of vectors in this way is called PARAFAC analysis.
  • the obtained independent vector a fk represents a frequency characteristic of vibration
  • b tk represents a temporal characteristic
  • c pk represents a spatial characteristic (this point will be further described later).
  • These features are also called frequency profile, temporal profile, and spatial profile, respectively.
  • the elements of the multidimensional data matrix handled in this embodiment are complex numbers. Therefore, it is divided into Sr ftp composed of real components and Si ftp composed of imaginary components, and PARAFAC analysis is performed on each of them (step SA-4 and step SA-6). The imaginary component will be described later in step SA-6.
  • T ftp represents an element of the predicted three-phase factor analysis model (Tucker3) (see Non-Patent Document 7). This shows the consistency between the elements calculated by PARAFAC and the predicted Tucker3 elements, and is 100% when decomposed by the ideal factor number. When the number of elements is small, the value is close to 100%, but as the number increases, it decreases rapidly to near 0% at a certain number. It is necessary to select the number of elements to take a value close to 100%.
  • SA-6 and SA-7 in FIG. 2 Similar to SA-4 and SA-5, three independent vectors aifk , bitk , and cipk can be obtained by targeting the imaginary part of the multidimensional vector data.
  • the magnitude (amplitude) of the vibration can be seen by calculating the square root of the square sum of the real and imaginary components.
  • the load time interval was 0.1 ms, and 8192 loads were performed while changing the amplitude.
  • the load signal has 8192 pieces of load data.
  • This weight signal is obtained by passing white noise created using random numbers through a filter W (s) of the following equation (9). That is, in this signal, it is possible to obtain a load (external force) close to a so-called 1 / f fluctuation that the amplitude decreases as the frequency becomes higher.
  • the cut-off frequency ⁇ c was 20 ⁇ rad / s.
  • FIG. 6 shows the acceleration at each point when the external force shown in FIG. 5 is applied to the beam 100 (corresponding to step SA-1 in FIG. 2).
  • the accelerations at points p 1 to p 5 are shown in order from the top of FIG.
  • white noise is mixed in the acceleration shown in FIG. 6 in order to simulate the observation noise.
  • FIG. 7 shows the absolute value, that is, the amplitude of each element in this complex data matrix.
  • the acceleration at points p 1 to p 5 is shown in order from the top.
  • the vertical axis in this figure represents the frequency as an index. That is, 1 indicates 10 Hz and 2 indicates 100 Hz.
  • the value increases as the color changes from black to white. That is, a white portion indicates that a large vibration exists.
  • FIG. 8 shows the frequency characteristics.
  • the upper diagram in FIG. 8 shows the result for the real part, and the lower diagram shows the result for the imaginary part. Looking at the peaking frequency, it is easy to see that the three vectors a f1 , a f2 , and a f3 represent the second-order mode, first-order mode, and third-order mode for both the real and imaginary parts. Recognize. In the figure, the subscripts r and i correspond to the real part and the imaginary part, respectively.
  • FIG. 9 and FIG. 10 represent temporal characteristics of the real part and the imaginary part, respectively.
  • b t1 , b t2 , and b t3 are represented in order from the top, and waveforms of the secondary mode, the primary mode, and the tertiary mode are shown, respectively.
  • the meanings of the subscripts r and i are the same as described above.
  • FIG. 11 shows the spatial characteristics of the real part.
  • cr p1 , cr p2 , and cr p3 are represented, and the second, first, and third-order mode shapes are shown, respectively.
  • the length of the beam is 1 m and FIG. 11 represents only the left half of the beam, it can be seen that an appropriate mode shape can be obtained by the vibration analysis of this embodiment. The same result is obtained for the imaginary part (not shown).
  • Chirp is a vibration whose frequency changes with time.
  • the acceleration is acquired as the vibration and the analysis is performed as in the above calculation example.
  • FIG. 13 shows a chirp-shaped point load.
  • the frequency of this vibration varies linearly from 1 Hz to 300 Hz.
  • the amplitude was 4e- t / 0.4085, and it was made smaller with time.
  • FIG. 14 shows the acceleration at each point when the external force shown in FIG. 13 is applied.
  • the accelerations at points p 1 to p 5 are shown in order from the top of FIG. From the first mode to the third mode, in which vibration is applied while sweeping the frequency from the low frequency, appears in order. In this case as well, white noise is mixed in the acceleration value in order to simulate the observation noise.
  • FIG. 16 shows three vectors a f1 , a f2 , and a f3 indicating frequency characteristics, and these represent the secondary mode, the primary mode, and the tertiary mode, respectively.
  • the upper figure in FIG. 16 represents the result of the real part
  • the lower figure represents the result of the imaginary part.
  • FIGS. 17 and 18 show three vectors b t1 , b t2 , and b t3 indicating temporal characteristics for the real part and the imaginary part, respectively.
  • the meanings of the subscripts r and i are the same as described above.
  • the first-order mode (b t2 ) appears from the beginning and gradually attenuates.
  • the secondary mode (b t1 ) and the tertiary mode (b t3 ) appear after the elapse of time.
  • the time in which each mode appears can be clarified.
  • FIG. 19 shows real-part vectors cr t1 , cr t2 , cr t3 indicating spatial features. These show that the spatial displacement (shape) in each mode is captured. The same result is obtained for the imaginary part (not shown).
  • FIG. 20 shows the calculation result. Not only can the characteristics of FIG. 15 be restored, but also noise can be removed, and as a result, a diagram in which only the mode of interest is extracted can be obtained.
  • the analysis technique described in the present embodiment can be executed by a computer by using a computer program that can be executed by the computer.
  • each functional element described above only needs to exist as a functional block, and does not need to exist as independent hardware.
  • a mounting method hardware or computer software may be used.
  • one functional element in the present invention may be realized by a set of a plurality of functional elements, and a plurality of functional elements in the present invention may be realized by one functional element.
  • the functional elements may be arranged at physically separated positions.
  • the functional elements may be connected by a network. It is also possible to realize functions or configure functional elements by grid computing.
  • the vibration applied to the beam has been described as an example.
  • the vibration applied to an object other than the beam can also be analyzed.
  • mechanical vibration is targeted as the analysis target.
  • the present invention is not limited to this, and it is also possible in principle to analyze acoustic vibration and electromagnetic wave vibration.
  • the wavelet transform is used in the analysis of the vibration data.
  • the present invention is not limited to this, and a short-time Fourier transform can also be used.
  • the frequency analysis unit only needs to be able to generate multidimensional vector data that is a function of time and frequency based on vibration data.
  • the real part and the imaginary part are respectively generated by the complex wavelet transform, and the PARAFAC analysis is performed for each.
  • wavelet transform generates either the real part or the imaginary part, or the absolute value, that is, the square root of the sum of the square of the real part and the square of the imaginary part. Analysis is also possible. However, if the phase information is lost, it becomes difficult to restore the original data from the data obtained by PARAFAC analysis.
  • the upper graph shows the result for the real part, and the lower graph shows the result for the imaginary part. It is a graph which shows the vector (real part) which shows the time characteristic of a vibration. It is a graph which shows the vector (imaginary part) which shows the time characteristic of a vibration. It is a graph which shows the vector which shows the spatial feature of a vibration. It is a graph which shows the wavelet transformation data reconstructed using the result of PARAFAC analysis. It is a graph which shows the vibration data added to a beam when the vibration input in this embodiment is made into a chirp shape. In the example of FIG. 13, it is a graph which each shows the vibration measured at each measurement point. In the example of FIG.
  • FIG. 13 it is a graph which each shows the result of the wavelet transformation with respect to each measurement data.
  • it is a graph which shows the change of the vector which shows a frequency characteristic.
  • the upper graph shows the result for the real part, and the lower graph shows the result for the imaginary part.
  • it is a graph which shows the vector (real part) which shows the time characteristic of a vibration.
  • it is a graph which shows the vector (imaginary part) which shows the time characteristic of a vibration.
  • it is a graph which shows the vector which shows the spatial characteristic of a vibration.
  • it is a graph which shows the wavelet transformation data reconfigure

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  • General Physics & Mathematics (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

L'invention concerne un dispositif et un procédé d'acquisition de caractéristiques concernant le changement temporel d'une oscillation. Une unité d'acquisition d'oscillation (1) acquiert des données d'oscillation dans une pluralité de positions. Une unité d'analyse de fréquence (2) analyse les données d'oscillation à l'aide de la conversion des petites ondes par exemple. Ainsi, il est possible de générer des données de vecteurs multidimensionnels en fonction du temps et de la fréquence. L'unité d'analyse de facteur multicouche (3) utilise les données de vecteurs multidimensionnels pour générer une pluralité de vecteurs indépendants. Au moins l'un des vecteurs générés par l'unité d'analyse de facteur multicouche (3) exprime la caractéristique temporelle de l'oscillation.
PCT/JP2009/064496 2008-08-22 2009-08-19 Dispositif d'analyse d'oscillation et procédé d'analyse d'oscillation WO2010021336A1 (fr)

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JP2008213549A JP2010048684A (ja) 2008-08-22 2008-08-22 振動解析装置及び振動解析方法
JP2008-213549 2008-08-22

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CN102538951A (zh) * 2011-12-30 2012-07-04 中国人民解放军后勤工程学院 一种检测自修复添加剂自修复效果的方法
JP6535208B2 (ja) * 2015-05-12 2019-06-26 株式会社豊田中央研究所 振動解析モデルの構造同定装置及びその同定方法

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Title
"Proceedings of the IEICE Conference", vol. 2003, 10 September 2003, article FUMIKAZU MIWAKEICHI ET AL.: "Parallel Factor Analysis ni yoru Noha no Kukan/Jikan/Shuhasu Seibun Bunkai to Shingo no Chushutsu", pages: 62 *
RASMUS BRO, PARAFAC. TUTORIAL AND APPLICATIONS, CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS, vol. 38, no. ISSUE, October 1997 (1997-10-01), pages 149 - 171 *

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