JPH045538A - Signal analyzing method using walsh transformation - Google Patents

Abstract

PURPOSE:To speedily and accurately extract a change in the state of a system, etc., by calculating the index in a sequence area according to fast Walsh transformation and detecting its variation. CONSTITUTION:The time history signal of a signal to be analyzed is Walsh- transformed WT (101) and then a Walsh spectrum W is found (102); and the index of at least one of a center alternation number Sc and an RMS alternation number Srms which are defined according to the Walsh spectrum W, and the variation factor K1 and kurtosis factor K2 of the spectrum distribution is calculated (103) and the feature of the signal to be analyzed is extracted from variation in the index.

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to a signal analysis method used for monitoring the condition of a vibration system, and more specifically, to a new index based on a Walsh spectrum for signal analysis. The present invention relates to a signal analysis method using Walsh transform that calculates .

[Conventional technology]

As the system deteriorates, vibration signals during operation often change in the time and frequency domains.

For example, when an impact occurs in a gap between moving mechanical elements, or within a bearing or gear, vibrations become intense. In this case, pulse-like acceleration occurs in the time domain, and high frequency components increase in the frequency domain.

The commonly used method for monitoring the condition of a vibrating system is as follows:
The purpose is to extract changes in the characteristics of the spectrum based on power spectrum analysis.

One of the effective parameters to express the characteristics of spectral distribution
One example is the average frequency. What is the average frequency?
It refers to the average number of times the zero level is crossed with a positive slope per unit time, and in the case of a steady ergodic irregular process where the average value is zero, the average frequency f is given by the following equation.

However, f is the frequency and 5(f) is the power spectral density function.

As described above, when a high frequency component appears due to a system failure or the like, this average frequency f becomes high.

This average frequency 11 is one efficient index for fault diagnosis, and two calculation methods are generally known. In other words, there are two methods: a method of analyzing the power spectrum based on fast Fourier transform (FFT), and a method of directly obtaining the signal from the time history and its differential process (time domain).
0operation). The latter calculation method is given by the following equation.

Here, si(・)=x (i+IL x (i), (
...0,1. ..., N-1) Δt [Problem to be solved by the invention] However, since the former method involves complicated complex number calculations,
The latter method is time consuming, and the latter method does not provide sufficiently accurate results using M-number digital operations to obtain differential signals.

An object of the present invention is to provide a signal analysis method using Walsh transform that can quickly and accurately extract features of a signal to be analyzed by calculating an index based on a Walsh spectrum.

[Means to solve the problem]

In order to solve the above-mentioned problems, the signal analysis method using Walsh transform according to the present invention performs Walsh transform on the time history signal of the signal to be analyzed, obtains a Walsh spectrum, and calculates a central alternating box defined based on the Walsh spectrum. 1i, an RMS alternation number, a spectral distribution variation factor, and a sharpness factor, and are configured to calculate the characteristics of the signal to be analyzed from changes in the index.

〔Example〕

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described in detail below with reference to the drawings and the like.

FIG. 1 is a diagram for explaining an embodiment of a signal analysis method using Walsh transform according to the present invention.

In this signal analysis method, as shown in Fig. 1, after the time history signal of the signal to be analyzed is subjected to Walsh transform -1 (101)
, the Walsh spectrum is obtained (102), and the central alternation number S defined based on the Walsh spectrum is
c, the number of RMS alternations 308, at least one index of 1 for the variation factor of the spectral distribution and 2 for the sharpness factor103) is calculated, and the characteristics of the signal to be analyzed are extracted from the changes in the index. .

The signals to be analyzed include vibration signals generated from the system,
For example, vibration acceleration detected by an accelerometer provided in the housing of a bearing can be given as an example.

The Walsh transform expands the signal to be analyzed into a Walsh function sequence. A Walsh function sequence is a square wave sequence arranged in order of the number of zero crossings. Taking the first four Walunyu functions -AL(s, t) as an example, the sequence shown in Figure 2(a) to (
The result is a function sequence as shown in d). In this way, since the Walsh transform is a binary signal, the main operations are only addition and subtraction, and compared to the Fourier transform, which uses a trigonometric function system, it is easier to implement in hardware and is more convenient for computer processing. It has overwhelming high speed.

The Walsh spectrum represents the distribution of signals in the sequence domain, and like the Fourier spectrum, necessary information can be obtained from the Walsh spectrum. For the N-point Walsh transform, (N
/2+1)-point Walsh spectrum W(s)
is given by the following equation.

w(0) = Wt”(0) W(1) = WT”(1)+W7”(2)−(
2)-Yent ”(3)+W7”(4)Yen(N/2-
1) = −□ ”(N-3)+wt ”(
N-2) W(N/2) -WT ”(N-1)
...(3) However, ga□(s
) is the Walsh transform of the time history signal. That is, Wt (s) = ΣWAL(s, t)X(i
)...(4) (s-01,2,-,N-1) However, X(i) (i-0,1,2,-,N-1) is a sample value of the system output.

Next, in order to quickly detect changes in the Walsh spectrum in the sequence domain, the following central alternation number S
c and the RMS (Root Mean 5 square) alternation number Sr's.

Here, the sequence domain is a Walsh transform domain. The number of alternations at this time is similar to frequency, and 1/2 of the number of zero crossings per unit time is defined as the average number.

Center number of alternations S,: Σ S, ・ −(S,) c − Σ K(S,) RMS number of alternations 5rai: ...(5) where S is the number of alternations and W(s; ) is the Walsh spectrum It is.

When these indicators correspond to physical concepts, the central alternation number Sc represents the center of the spectral figure, and the RMS alternation number S
rs represents the radius of rotation. The more high alternating number components there are, the larger the center and radius of rotation become.

In the case of fault diagnosis, dimensionless factors are often used, but
These have the characteristics of being sensitive to failure information but not sensitive to the driving environment. Therefore, equation (5), (6
) In addition to the index defined in ), two dimensionless factors, 1 for the variation factor of the spectral distribution and 2 for the skewness factor, are defined by the following equation.

The variation factor is 1: Σ s, Z · -(S,) The sharpness factor is 2: Σ s, 4 · - (s8) These dimensionless factors are used to indicate the operating state. When the state of the system becomes abnormal, pulse-like vibrations appear, and high-frequency components increase, the high-dimensional moment increases significantly more than the low-dimensional moment, and each of the defined factors takes a large value, so those factors The characteristics of the signal to be analyzed can be extracted from the changes in .

The inventors of the present invention conducted a computer simulation using a signal analysis method using this Walsh transformation.

In this example, the index was calculated using simulation data of the output of a nonlinear system receiving stationary regular white noise input. As shown in FIG. 3, these models are one-degree-of-freedom systems, and are a collision model and a Duffing model expressed by the cube of displacement. In the former case,
It is assumed that a mass point collides with a more rigid outer wall due to large amplitude vibration. The number of samplings N is 16
384 (=2”), and the sampling interval Δt is 0
, 1 second.

As the dimensionless nonlinear parameter e (determined by the nonlinear amount and input level) in these nonlinear systems increases, the equivalent stiffness of the system increases, and thus the high frequency component of the output increases. Therefore, the nonlinear parameter e
It is expected that as the number increases, the index defined earlier, such as the number of central alternations in the output signal, will increase.

The time history of the output corresponding to each nonlinear parameter e is shown in FIG. 4 (impact model) and FIG. 5 (Duffing model). The results of determining indicators from these data are shown in Tables 1 and 2.

Table 1 (Collision model) 1124.94B1 1834.06721
216.9416 1955.1214.2
8064987. 27781355 2 3.8425674 3.5257480 0.5 . 56598985 5.21495! IH Table 2 (Duffing model) 0.5 1427.9454 2207.0627 Based on these calculation results, as shown in Figure 6 (Collision model) and Figure 7 (Duffing model), Four fingers ij' for changes in dimensionless nonlinear parameter e
Distribution curves for S, , S, , , Kl, and 2 were obtained. In these figures, the value when e=0.1 is set to 0, and the rate of increase from there is expressed.

From these curves, as the nonlinear parameter e increases,
It can be seen that for both models, an increase of 1 in the variation factor becomes extremely large. Next, the change in the sharpness factor of 2 is large and is particularly sensitive in the Duffing model, but it also shows a clear increasing tendency in the collision model when the nonlinear parameter e takes a large value. Furthermore, it can be seen that the central alternation number S, is more sensitive than the RMS alternation number Sr□ in both models.

Therefore, depending on the characteristics of the nonlinear model or the magnitude of its nonlinear parameters, the most sensitive index among the four indexes defined here may be selected as appropriate, and one or more of them may be used in combination.

Here, simulation results obtained by the analysis method of the present invention and a conventional method will be compared.

FIG. 8 shows the rate of increase in the RMS alternation number 5FlIs and the average frequency f calculated by FFT with respect to changes in the nonlinear parameter e. RMS alternation number Sr
It can be seen that ++s corresponds to the average frequency f, but is clearly more sensitive than the average frequency f.

These results revealed that as the nonlinear parameters increase, the values of these indicators increase in the sequence domain, which is effective for monitoring the system status.

〔Effect of the invention〕

As explained in detail above, according to the present invention, indicators in the sequence domain are calculated based on fast Walsh transform and changes thereof are detected, so changes in the state of the system can be extracted quickly and accurately. This has the effect of allowing you to do so.

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing an embodiment of the signal analysis method using the Walsh transform according to the present invention, Fig. 2 is a diagram for explaining the Walsh transform, and Fig. 3 is a collision model used in the simulation. FIG. 4 and FIG. 5 are diagrams showing time history signals corresponding to these models, and FIGS. 6 to 8 are diagrams showing simulation results. Agent Patent Attorney Kama 1) Hisao

Claims (1)

[Claims] After performing the Walsh transform on the time history signal of the signal to be analyzed, a Walsh spectrum is obtained, and at least one index of the number of central alternations, the number of RMS alternations, the variation factor of the spectral distribution, and the kurtosis factor is determined based on the Walsh spectrum. A signal analysis method using Walsh transformation, which is configured to perform calculations and extract features of the signal to be analyzed from changes in the index.