# US 5,710,715 A · Vibration analysis method

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- Number: US 5,710,715 A
- Document ID: US5710715A
- Status: Granted
- Kind: A
- Application number: 08/507,925
- Filed: 1995-07-27
- Granted: 1998-01-20
- Earliest claimed: 1994-07-28
- Assignees: Matsushita Electric Industrial Co., Ltd.
- Inventors: Motoshi Shitanda
- Web page: https://patentgrep.com/patent/US5710715A

## CPC

- G01M 15/12: by monitoring vibrations
- G01H 1/003: {of rotating machines (G01H1/10 takes precedence)}
- G01L 23/225: {circuit arrangements therefor}
- G05B 23/024: {Quantitative history assessment, e.g. mathematical relationships between available data; Functions therefor; Principal component analysis [PCA]; Partial least square [PLS]; Statistical classifiers, e.g. Bayesian networks, linear regression or correlation analysis; Neural networks}
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01H: MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01L: MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE (weighing G01G)
- G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G)

## Abstract

A vibration analysis method for detecting abnormalities by analyzing a vibration waveform. The method includes the steps of, in a plurality of observation time points {t.sub.j } composed of a number n of specified time points t.sub.j (j=1 to n) counted from a start time point t.sub.0, detecting displacements of a vibration wave f.sub.j (j=1 to n) at the individual time points of the plurality of observation time points, and comparing points in an n-dimensional space composed of the displacements, detected at the individual observation time points, with points in the n-dimensional space of a vibration waveform that are designated as being normal.

## Claims

### Claim 1

A vibration analysis method for detecting abnormalities by analyzing a vibration waveform, said method comprising the steps of:
detecting displacements of a vibration waveform f.sub.j (j=1 to n) at a set of observation time points {t.sub.j }, wherein the set of observation time points {t.sub.j } are of a specified number n wherein t.sub.j (j=1 to n) with a start time point of t.sub.0 ;
calculating .alpha. which is a characteristic quantity of the vibration waveform by substituting .psi.(t), which is a function of time t and is descriptive of a specified phenomena, into a following equation with .xi..sub.+, .xi..sub.0, and .xi..sub.- being values such that .xi..sub.+ +.xi..sub.0 +.xi..sub.- =0: ##EQU10## where .psi.(t.sub.j) is a function of time t.sub.j ; limiting an allowable range in the n-dimensional space based upon .alpha.;
comparing points in an n-dimensional space of the displacements detected at the set of observation time points at said detecting step with points in the n-dimensional space of a vibration waveform that is designated as being normal; and
determining whether points in the n-dimensional space compared at said comparing step are abnormal, wherein a point is determined to be abnormal when the comparison falls outside the allowable range.

### Claim 2 (depends on 1)

The vibration analysis method of claim 1, further comprising the step of displaying the results of said determining step.

### Claim 3 (depends on 1)

The vibration analysis method of claim 1, wherein .psi.(t) is defined by the following equation with k being a real number: ##EQU11##

### Claim 4 (depends on 3)

The vibration analysis method of claim 3, further comprising the steps of:
providing a plurality of sets of the observation time points;
setting the real number k with respect to each of the sets of observation time points; and
performing said detecting, calculating, limiting, comparing, and determining steps for the plurality of sets of the observation time points.

### Claim 5 (depends on 1)

The vibration analysis method of claim 1, wherein .psi.(t) is defined by the following equation with k being a real number:
.psi.(t)=exp(-kt).

### Claim 6 (depends on 5)

The vibration analysis method of claim 5, further comprising the steps of:
providing a plurality of sets of the observation time points;
setting the real number k with respect to each of the sets of observation time points; and
performing said detecting, calculating, limiting, comparing, and determining steps for the plurality of sets of the observation time points.

### Claim 7 (depends on 1)

The vibration analysis method of claim 1, further comprising the steps of:
providing a plurality of sets of the observation time points;
setting the function .psi.(t) with respect to the plurality of the sets of the observation time points; and
performing said detecting, calculating, limiting, comparing, and determining steps for the plurality of sets of the observation time points.

### Claim 8

A vibration analysis method for detecting abnormalities by analyzing a vibration waveform, said method comprising the steps of:
detecting displacements of a vibration waveform f.sub.j (j=1 to n) at a set of observation time points {t.sub.j }, wherein the set of observation time points {t.sub.j } are of a specified number n wherein t.sub.j (j=1 to n) with a start time point of t.sub.0 ;
calculating .beta. which is a characteristic quantity of the vibration waveform by substituting .psi.(t), which is a function of time t and is descriptive of a specified phenomena, into a following equation with .xi..sub.+, .xi..sub.0, and .xi..sub.- being values such that .xi..sub.+ +.xi..sub.0 +.xi..sub.- =0: ##EQU12## where .psi.(t.sub.j) is a function of time t.sub.j ; limiting an allowable range in the n-dimensional space based upon .beta.;
comparing points in an n-dimensional space of the displacements detected at the set of observation time points at said detecting step with points in the n-dimensional space of a vibration waveform that is designated as being normal; and
determining whether points in the n-dimensional space compared at said comparing step are abnormal, wherein a point is determined to be abnormal when the comparison falls outside the allowable range.

### Claim 9 (depends on 8)

The vibration analysis method of claim 8, further comprising the step of displaying the results of said determining step.

### Claim 10 (depends on 8)

The vibration analysis method of claim 8, wherein .psi.(t) is defined by the following equation with k being a real number: ##EQU13##

### Claim 11 (depends on 10)

The vibration analysis method of claim 10, further comprising the steps of:
providing a plurality of sets of the observation time points;
setting the real number k with respect to each of the sets of observation time points; and
performing said detecting, calculating, limiting, comparing, and determining steps for the plurality of sets of the observation time points.

### Claim 12 (depends on 8)

The vibration analysis method of claim 8, wherein .psi.(t) is defined by the following equation with k being a real number:
.psi.(t)=exp(-kt).

### Claim 13 (depends on 12)

The vibration analysis method of claim 12, further comprising the steps of:
providing a plurality of sets of the observation time points;
setting the real number k with respect to each of the sets of observation time points; and
performing said detecting, calculating, limiting, comparing, and determining steps for the plurality of sets of the observation time points.

### Claim 14 (depends on 8)

The vibration analysis method of claim 8, further comprising the steps of:
providing a plurality of sets of the observation time points;
setting the time function .psi.(t) with respect to the plurality of sets of the observation time points; and
performing said detecting, calculating, limiting, comparing, and determining steps for the plurality of sets of the observation time points .