JP2958568B2 - Signal analysis method using Walsh transform - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for analyzing a signal used for monitoring the state of a vibration system, and more particularly, to a new index based on a Walsh spectrum for signal analysis. And a signal analysis method using a Walsh transform that calculates

[Conventional technology]

When the system deteriorates, the operating vibration signal often changes in the time domain and the frequency domain.

For example, when an impact is generated in a gap between moving mechanical elements, or when an impact is generated in a bearing or a gear, vibration is increased. In that case, a pulse-like acceleration occurs in the time domain, and the high-frequency component increases in the frequency domain.

A common method for monitoring the condition of a vibrating system is to extract changes in its spectral features based on power spectrum analysis.

One of the effective parameters for expressing the characteristics of the spectral distribution is an average frequency. The average frequency refers to the average number of times crossing the zero level with a positive slope per unit time, when the steady ergodic random process average value takes zero, the average frequency f _m is given by the following equation.

Here, f is a frequency, and S (f) is a power spectrum density function.

As described above, such as by failure of the system, the high-frequency component appears, the average frequency f _m becomes high.

The average frequency f _m is an efficient one indicator in the diagnosis of faults, usually two calculation methods are known. That is, a method of analyzing from a power spectrum based on a fast Fourier transform (FFT), and a method of directly obtaining from a signal of a time history and its differentiation process (Time Domain Operation)
It is. The calculation method of the latter is given by the following equation.

here, [Problems to be Solved by the Invention] However, the former method involves a complicated complex number calculation, and therefore is time-consuming, and the latter method is sufficiently accurate in discrete digital operation to obtain a differential signal. No result.

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

[Means for solving the problem]

In order to solve the above problem, a signal analysis method using a Walsh transform according to the present invention performs a Walsh transform on a time history signal of a signal under analysis, obtains a Walsh spectrum, and determines a center alternation defined based on the Walsh spectrum. At least one index of the number, the number of RMS alternations, the variation factor of the spectrum distribution and the sharpness factor is calculated, and the feature of the analyzed signal is extracted from the change of the index.

〔Example〕

Hereinafter, the present invention will be described in detail with reference to the drawings and the like based on embodiments.

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

The signal analysis method, as shown in FIG. 1, after the time history signal of the analyzed signal is Walsh transform W _T (101),
Calculated Walsh spectrum W (1029, calculated at least one indicator of the Walsh spectrum W central alternating number S _c as defined on the basis of, RMS alternating number S _rms, variation factors of the spectral distribution K1 and kurtosis level factor K2 ( 103), the characteristic of the analyzed signal is extracted from the change of the index.

Examples of the analyzed signal include a vibration signal generated from the system, for example, a vibration acceleration detected by an accelerometer provided in a housing of the bearing.

The Walsh transform develops a signal under analysis into a Walsh function sequence. The Walsh function sequence is a square wave sequence arranged in the order of the number of zero crossings, and taking the first four Walsh transform functions MAL (s, t) as an example, FIG.
The function sequence is as shown in FIG. As described above, since the Walsh transform is a binary signal, the main operation is only addition and subtraction, and it is easy to implement hardware as compared with the Fourier transform using a trigonometric function system. Has overwhelming high speed.

The Walsh spectrum represents the distribution of a signal in the sequence domain, and necessary information can be obtained from the Walsh spectrum, similarly to the Fourier spectrum. In the case of N-point Walsh transform,
(N / 2 + 1) -point Walsh spectrum W
(S) is given by the following equation.

Here, W _T (s) is a Walsh transform of the time history signal. That is, Here, X (i) (i = 0, 1, 2,..., N−1) is a sample value of the system output.

Next, in order to detect the change of the Walsh spectrum in the sequence region at high speed,
An index called S _c and an RMS (Root Mean Square) alternation number S _rms is defined.

Here, the sequence area is a Walsh transform area. The number of alternations at this time is similar to the frequency, and half of the number of zero crossings per unit time is defined as an average number.

Central alternation number S _c : RMS alternation number S _rms : Here, s _i is an alternation number, and W (s _i ) is a Walsh spectrum.

Made to correspond to these indicators physical concepts, central alternating number S _c represents the center of the spectral shape, RMS alternating number S _rms
Represents the radius of gyration. The center and the turning radius increase as the number of components with a high alternation number increases.

In the case of failure diagnosis, dimensionless factors are often used, but have a feature that they are sensitive to such failure information and insensitive to the driving environment. Therefore, equation (5),
In addition to the index defined in (6), two dimensionless factors of a spectral distribution variation factor K1 and a sharpness factor K2 are defined by the following equation.

Variable K1: Sharpness factor K2: These dimensionless factors are used as indicators of operating conditions. When the state of the system becomes abnormal, a pulse-like signal appears, and the high-frequency component increases, the high-dimensional moment increases more rapidly than the low-dimensional moment, and each defined factor takes a large value. From the change in the characteristic of the analyzed signal.

The present inventors performed computer simulation by a signal analysis method using the Walsh transform.

In this embodiment, using the simulation data of the output of the nonlinear system which receives the stationary normal white noise input,
Index calculations were performed. These models are one-degree-of-freedom systems as shown in FIG. 3, and are a collision model and a duffing system model represented by the cube of displacement. In the former case, it is assumed that the mass point collides with the outer wall having higher rigidity due to the large amplitude vibration. The sampling number N is
At 16384 (= 2 ¹⁴ ), the sampling interval Δt is 0.1 second.

When the dimensionless nonlinear parameter e (determined by both the nonlinearity and the input level) in these nonlinear systems increases, the equivalent stiffness of the system increases, and the high-frequency component of the output increases. Therefore, as the nonlinear parameter e increases, it is expected that the previously defined index such as the number of center alternations of the output signal will increase.

The output time histories corresponding to the respective nonlinear parameters e are shown in FIG. 4 (collision model) and FIG. 5 (duffing model). Tables 1 and 2 show the results of obtaining indices from these data.

Based on these calculation results, as shown in FIG. 6 (collision model) and FIG. 7 (duffing model), four indices for the change of the dimensionless nonlinear parameter e
The distribution curves of S _c , S _rms , K1, and K2 were obtained. In these figures, the value when e = 0.1 is set to 0, and the rate of increase from there is shown.

From these curves, it can be seen that as the nonlinear parameter e increases, the increase in the variation factor K1 in both models becomes extremely large. Next, the sharpness factor K2 has a large change, and is particularly sensitive in the duffing model. However, the collision model also shows a clear increasing tendency when the nonlinear parameter e takes a large value. The center alternation number _Sc is the RMS alternation number S for both models.
It turns out that it is more sensitive than _rms .

Therefore, the most sensitive index among the four indexes defined here may be appropriately selected according to the characteristics of the non-linear model or the magnitude of the non-linear parameter, and may be used alone or in combination of two or more.

Here, the analysis results of the analysis method of the present invention and the simulation results of the conventional method are compared.

Figure 8 is a graph showing the RMS alternating number S _rms to changes in non-linear parameters e, an increase in the average frequency f _m which is calculated by the FFT. The RMS alternation number S _rms is the average frequency f
but which corresponds to _m, it is understood that clearly more sensitive than average frequency f _m.

From these results, it has been clarified that the values of these indices increase in the sequence region as the nonlinear parameters increase, which is effective for monitoring the system state.

〔The invention's effect〕

As described above in detail, according to the present invention, the index in the sequence area is calculated based on the fast Walsh transform and the change is detected, so that the change in the state of the system and the like can be extracted quickly and accurately. Can,
This has the effect.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an embodiment of a signal analysis method using Walsh transform according to the present invention, FIG. 2 is a diagram for explaining Walsh transform, and FIG. 3 is a diagram showing a collision model used for simulation. FIGS. 4 and 5 show the duffing model, FIGS. 4 and 5 show time history signals corresponding to those models, and FIGS. 6 to 8 show simulation results.

Claims (1)

(57) [Claims] A Walsh spectrum is obtained from a time history signal of a signal under analysis, a Walsh spectrum is obtained, and a center alternation number, an RMS alternation number, a variation factor of a spectrum distribution and a sharpness factor defined based on the Walsh spectrum. A signal analysis method using a Walsh transform configured to calculate at least one index and extract characteristics of the analyzed signal from a change in the index.