WO2010021336A1

WO2010021336A1 - Oscillation analysis device and oscillation analysis method

Info

Publication number: WO2010021336A1
Application number: PCT/JP2009/064496
Authority: WO
Inventors: 公彦中野
Original assignee: 国立大学法人東京大学
Priority date: 2008-08-22
Filing date: 2009-08-19
Publication date: 2010-02-25
Also published as: JP2010048684A

Abstract

Provided are device and a method which can acquire characteristics concerning a temporal change of oscillation. An oscillation acquisition unit (1) acquires oscillation data in a plurality of positions. A frequency analysis unit (2) analyzes oscillation data by using the wavelet conversion, for example. Thus, it is possible to generate multi-dimension vector data as a function of time and frequency. A multi-layer factor analysis unit (3) uses the multi-dimension vector data to generate a plurality of independent vectors. At least one of the vectors generated by the multi-layer factor analysis unit (3) expresses the temporal characteristic of the oscillation.

Description

Vibration analysis apparatus and vibration analysis method

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.

Conventionally, Fourier analysis represented by FFT (Fast Fourier Transform) is known as a method for analyzing vibration. By using the Fourier analysis, it is possible to know characteristics related to the frequency of vibration.

However, Fourier analysis has the characteristic that it is difficult to know the characteristics related to temporal changes in vibration.

Therefore, 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.

On the other hand, PARAFAC, also called multi-layer factor analysis, is a method of decomposing a time-varying spectrum of a signal measured in multiple channels into multi-dimensions with space, frequency, time, etc. as axes (non-patent document 1 below). 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). In recent years, 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 α, β, θ bands, etc. Patent Document 2). This method has high temporal resolution and is suitable for measurement in a moving environment, and is expected to be developed in the future.
R. Bro, PARAFAC.Tutorial & applications, Chemometrics and Intelligent Laboratory Systems, 38 (1997), 149-171. F. Miwakeichi, E. Martinez-Montes, PA Valdes-Sosa, N. Nishiyama, H. Mizuhara, and Y. Yamaguchi, Decomposing EEG data into space-time-frequency components using Parallel Factor Analysis, NeuroImage 22 (2004), 1035 -1045. Akio Nagamatsu, mode analysis, Baifukan. Hideki Toyoda, Covariance Structure Analysis [Application], Asakura Shoten.

The present invention has been made in view of such a situation. 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.

(Item 1)
It has a vibration acquisition unit, a frequency analysis unit, and a multilayer factor analysis unit,
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.

In the present invention, the vibration to be analyzed is, for example, mechanical vibration. However, the vibration may be a vibration of sound or electromagnetic waves in addition to the mechanical vibration.

(Item 2)
The vibration analysis apparatus according to item 1, wherein the multidimensional vector data is generated by wavelet transform on the vibration data.

(Item 3)
The vibration analysis apparatus according to item 1, wherein the multidimensional vector data is generated by a short-time Fourier transform on the vibration data.

(Item 4)
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.

(Item 5)
A computer program for causing a computer to execute each step according to item 4.

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.

According to the present invention, it is possible to provide an apparatus and a method capable of acquiring characteristics related to the temporal change of vibration.

Hereinafter, the configuration of a vibration analysis apparatus according to an embodiment of the present invention will be described with reference to FIG. In this embodiment, an example of an apparatus for analyzing mechanical vibration is shown.

(Configuration of vibration analyzer)
The vibration analysis apparatus according to the present embodiment 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. As vibration data, in addition to acceleration, data of an image taken by a speed, displacement, and high-speed camera can be used. As the vibration acquisition unit 1, 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. Here, at least one of the plurality of vectors generated by the multilayer factor analysis unit 3 represents a temporal characteristic of vibration.

The operation of each part in the apparatus of this embodiment will be described in more detail in the description of the vibration analysis method described below.

(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.

(SA-1 in FIG. 2)
First, vibration is applied to the beam. As shown in FIG. 3, the beam 100 is a so-called simple support beam.

It is assumed that the point load vibration f ₀ is applied to the beam 100. 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. Also, 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 ω _n is the natural angular frequency of the n-th mode.

Here, k _n is determined by the following equation.

Here, 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. In the present embodiment, the third mode is taken into consideration. That is, calculation is performed with N = 3.

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.

(SA-2 and SA-3 in FIG. 2)
Next, the frequency analysis unit 2 performs frequency analysis as follows. In this embodiment, wavelet transform is used as frequency analysis.

In this embodiment, before performing multi-layer factor analysis (so-called PARAFAC analysis), which will be described later, 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.

In this equation (3), Ψ (t) represents a mother wavelet. Various mother wavelets have been proposed. In this embodiment, 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). In equation (4), f _b is a bandwidth parameter and f _c is a center frequency. Here, f _b = 2 and f _c = 1.

If the data t is time history data with an interval dt, the scale a is converted to a frequency f (Hz) by the following equation (5). Thereby, 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).

Note that so-called PARAFAC analysis is generally performed on time-varying spectrums. For this reason, in the conventional PARAFAC analysis, the absolute value of a complex multidimensional data matrix is often the object of analysis (see Non-Patent Document 2). However, in order to leave the phase information, in this embodiment, 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.

(SA-4 and SA-5 in FIG. 2)
The multilayer factor analysis unit 3 performs multilayer factor analysis (so-called PARAFAC analysis) on the multidimensional vector data. A schematic image of PARAFAC analysis is shown in FIG.

Here, 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: Consider separating into two vectors a _f , b _t and c _p . Here, k represents a factor, and N _k represents the number of factors.

However, 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 ε. The process of separating a multidimensional data matrix into a number of vectors in this way is called PARAFAC analysis.

Here, the obtained independent vector a _fk represents a frequency characteristic of vibration, b _tk represents a temporal characteristic, and 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.

Here, when performing PARAFAC analysis, it is necessary to determine an appropriate number of factors N _k . In other words, it is necessary to decide how many vectors to separate. Increasing the number of factors will reduce the residual, but too much will fit too much, so you need to decide on an appropriate number. The method of deriving the number of factors adapted by the Core consistency shown in the following formula (8) is generally applicable.

Here, 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%.

In this way, three independent vectors ar _fk , br _tk , cr _pk can be obtained (SA-5 in FIG. 2).

(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.

(Calculation example)
Hereinafter, more specific examples will be described using calculation examples.

(Random wave input)
First, a point load (vibration) as shown in FIG. The load time interval was 0.1 ms, and 8192 loads were performed while changing the amplitude. In other words, in this example, 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 ω _c was 20π 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. In this calculation example, white noise is mixed in the acceleration shown in FIG. 6 in order to simulate the observation noise.

Subsequently, a complex wavelet transform was performed on these observed accelerations (corresponding to step SA-2 in FIG. 2). Thereby, the complex data matrix S (N _f x N _t x N _p ) can be obtained. 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. As a result of this conversion, it can be seen that there are vibrations near the primary, secondary, and tertiary natural frequencies (23.2, 92.9, 208.9 Hz).

Next, the complex data matrix was divided into a real part and an imaginary part, and PARAFAC analysis was performed with a factor of 3 (corresponding to steps SA-4 and SA-6 in FIG. 2). 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.

«Core consistency in this calculation example is 100% in both the real and imaginary parts, and the number of factors is appropriate. In addition, since it is a numerical calculation that only considers up to the third-order mode, it can easily be seen that it is best to set the number of factors to 3, but for example, when performing PARAFAC processing with the number of factors set to 4 The real part drops to 88.6% and the imaginary part drops to 86.1%. Even if the number of modes is unknown in experiments or the like, it is possible to search for a suitable number of factors for this analysis method.

FIG. 9 and FIG. 10 represent temporal characteristics of the real part and the imaginary part, respectively. In these drawings, 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. There is no significant difference between the real part and the imaginary part except that there is a phase difference. According to these figures, it is possible to understand well the time change of the strength in which each mode appears.

FIG. 11 shows the spatial characteristics of the real part. In order from the top, cr _p1 , cr _p2 , and cr _p3 are represented, and the second, first, and third-order mode shapes are shown, respectively. Considering that 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).

(Data recovery)
In order to consider the validity of the vibration analysis in this embodiment, an attempt is made to restore vibration data applied to the beam using the analysis result. The vectors a _fk , b _tk , and c _pk obtained from the PARAFAC analysis are multiplied according to the above equation (6), and the square sum of squares of the obtained real part and imaginary part is calculated. Thereby, data similar to that in FIG. 7 can be restored. The restoration result is shown in FIG. When the results shown in FIG. 12 are compared with the data of FIG. 6, the results are almost the same. Rather, according to the result shown in FIG. 12, noise is excluded and only the mode of interest is extracted.

(Calculation example using chirp input)
Next, a calculation example when chirp is used as an input of vibration will be described below. Chirp is a vibration whose frequency changes with time. In the following calculation example, 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. During the time to apply vibration in the simulation (from 0 to 0.8191 seconds), 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.

Complex wavelet transform was performed on these observed accelerations. The absolute value of the conversion result is shown in FIG. In FIG. 15, the acceleration at points p ₁ to p ₅ is shown in order from the top. According to these, it can be seen that vibrations in the vicinity of the primary, secondary and tertiary natural frequencies (23.2, 92.9, 208.9 Hz) appear in order.

After that, PARAFAC analysis was performed with a factor of 3, and it was decomposed into 3 components. 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. In addition, the upper figure in FIG. 16 represents the result of the real part, and 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. In these figures, the first-order mode (b _t2 ) appears from the beginning and gradually attenuates. On the other hand, the secondary mode (b _t1 ) and the tertiary mode (b _t3 ) appear after the elapse of time. With the analysis method of the present embodiment, 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).

The vectors a _fk , b _tk , and c _pk obtained from the analysis in this calculation example were multiplied as in the above equation (6) to calculate the square sum of squares of the real part and the imaginary part. This should be able to restore the characteristics of FIG. 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.

In this calculation example, the natural frequency, the mode shape, and the temporal change of the dominant mode were clearly 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.

Note that the description of the embodiment and the examples is merely an example, and does not indicate a configuration essential to the present invention. The configuration of each part is not limited to the above as long as the gist of the present invention can be achieved.

For example, each functional element described above only needs to exist as a functional block, and does not need to exist as independent hardware. As a mounting method, hardware or computer software may be used. Furthermore, 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.

Further, the functional elements may be arranged at physically separated positions. In this case, the functional elements may be connected by a network. It is also possible to realize functions or configure functional elements by grid computing.

In the above embodiment, the vibration applied to the beam has been described as an example. However, the vibration applied to an object other than the beam can also be analyzed. Further, in the above-described embodiment, mechanical vibration is targeted as the analysis target. However, the present invention is not limited to this, and it is also possible in principle to analyze acoustic vibration and electromagnetic wave vibration.

In the embodiment, the wavelet transform is used in the analysis of the vibration data. However, the present invention is not limited to this, and a short-time Fourier transform can also be used. In short, 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.

In the above embodiment, the real part and the imaginary part are respectively generated by the complex wavelet transform, and the PARAFAC analysis is performed for each. However, if phase information is not required, 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.

It is a block diagram for demonstrating the schematic structure of the vibration analyzer which concerns on one Embodiment of this invention. It is a flowchart for demonstrating the whole flow of the vibration analysis method which concerns on one Embodiment of this invention. It is explanatory drawing for demonstrating an example of the beam which adds a vibration. It is explanatory drawing for demonstrating the method of the PARAFAC analysis used in this embodiment. It is a graph which shows an example of the vibration added to a beam. It is a graph which shows the vibration measured at each measurement point, respectively. It is a graph which shows the result of the wavelet transformation with respect to each measurement data, respectively. 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 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. 13, it is a graph which each shows the result of the wavelet transformation with respect to each measurement data. In the example of FIG. 13, 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. In the example of FIG. 13, it is a graph which shows the vector (real part) which shows the time characteristic of a vibration. In the example of FIG. 13, it is a graph which shows the vector (imaginary part) which shows the time characteristic of a vibration. In the example of FIG. 13, it is a graph which shows the vector which shows the spatial characteristic of a vibration. In the example of FIG. 13, it is a graph which shows the wavelet transformation data reconfigure | reconstructed using the result of the PARAFAC analysis.

Claims

It has a vibration acquisition unit, a frequency analysis unit, and a multilayer factor analysis unit,
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.
The vibration analysis apparatus according to claim 1, wherein the multidimensional vector data is generated by wavelet transform on the vibration data.
The vibration analysis apparatus according to claim 1, wherein the multidimensional vector data is generated by a short-time Fourier transform on the vibration data.
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.
A computer program for causing a computer to execute each step according to claim 4.